TL;DR: copy on write
First of all there's nothing wrong with your story having a time paradox, in fact certain stories require it. Trying to prevent a paradox is a valid motivation for a crisis, timestream changes can be an interesting way to add complications, etc. However for some stories you may want it free of paradox and that's more tricky than it sounds so I thought I would detail how this can be done (option #3 is the only real way).
First I need to explain what the issue is. For a single timeline that can be altered by traveling backwards in time there are 2 paradoxes that arise: a grandfather paradox and a bootstrap paradox. The grandfather paradox is the most commonly talked about paradox (and is normally just called a "time paradox" but that would be confusing). A grandfather paradox is often described as "what happens if I go back in time and kill my grandfather before my father was conceived?" The problem is that if there is a single timeline (by now you may have guessed the solution) on which you go backwards you can contradict it. If you kill your grandfather then you couldn't've been born which means you couldn't've killed him which contradicts the original action and thus the timeline is in an invalid state.
A bootstrap paradox is sort of the opposite. An example would be that you have a necklace that has been passed down from your great grandfather. You hear a story that he got it from a time traveler who turns out to be you. In an attempt to avoid a grandfather paradox you go back in time and give the necklace to your great grandfather. The necklace's place on the timeline is a nice circle which appears to be fixed but who created the necklace? How old is it? This necklace exists because it already exists. This is a causation paradox (which requires backwards time travel).
Notice that if you go back in time and do something then it will either cause a grandfather paradox (because the event wasn't supposed to happen) or a bootstrap paradox (because it was supposed to happen). You may say "I promise not to do anything important" but that's not good enough. Even something as simple as stepping on an ant is an event that happened and thus would cause either paradox but it's more extreme than that: every breath you take, every photon of light you absorb, every air molecule you displace. It's impossible to exist in any tangible way without causing a paradox.
However there are solutions which I will do from least useful to most. The first point (option #0) is to not do time travel at all which works but doesn't meet the criteria of "paradox free time travel" and thus is not considered an option. The first actual option (which isn't much better) is to do forward only time travel. These paradoxes only occur from going backwards, going forward causes no issues as long as the traveler never returns (by going backwards). You could make a story of someone going into the far future and be unable to go back and there would be no paradox (he absolutely can't go back to "his time" since that would cause a paradox with the present he's currently in). In fact this has been demonstrated to be possible in real life (only going forward a few seconds) and thus forward only time travel is an undebatable scientific occurrence that's iron clad against any paradox.
Option #2 is to have the past be "read only" such that it can be seen but nothing can be changed. The man who goes back will be as though he is intangible and absolutely nothing he does makes any difference. For this to work the time travel device would need to duplicate the photons so he can see them (in addition to the past photons which the past objects interacted with) and the same is true for all his senses. You may wonder if this is actually time travel or just watching a movie of something that happened in the past. You can describe it as backwards time travel but it doesn't really feel like it is.
This leaves the only real option #3 which is complicated but can be summed up as "copy on write". The 2 paradoxes hinge on the phrase "a single timeline that can be altered by traveling backwards in time." Option #1 disallowed traveling backwards, option #2 disallowed altering, and option #3 doesn't use a single timeline. Whenever someone travels back in time by any amount the timeline is copied and they are placed in the new one. Traveling forward in time remains in the same timeline. Basically the past of each timeline is unchangeable but a copy can be changed in any way without paradox. This model allows meeting copies of yourself since if you travel back in time to a point you existed the entire past is copied including your body. If you don't like what you've changed you can go back and murder your copy who was about to change it (this doesn't affect the previous timeline you were in) or go back right before he got there and have no copy show up (since only the past is copied). You can get as many copies of yourself as you like and if you'd like to return to normal you can travel back to before you touched anything then forward in that copy to your normal time to get an equivalent to your original assuming your brief tangibility didn't affect much. You could also permit returning to a timeline as long as the point of return is during or after what is considered the present for that timeline (the present being the last point in that timeline that has been visited by anyone).
Option #3 sounds complicated but allows for basically everything and should be easy to use. In fact if you never explain that copies are being made this time travel model will "just work" and still allows things like "we need to stop this event or we are screwed" for the timeline you are in. That said this model (as is) doesn't allow someone to be aware that the timeline has changed (since it's a copy, their own timeline hasn't changed) and again a crisis like "if we don't prevent this time paradox it will be the end of time itself" would require a paradox based model.
Note that being able to predict the future causes no time paradox. It doesn't matter if the prediction is contradicted. Unlike traveling to the future and back which causes issues because it wasn't a prediction, it actually happened and things aren't supposed to un-happen.
Professor Farnsworth: Your grandfather?! Stay away from him, you dim-witted monkey! You mustn't interfere with the past! Don't do anything that affects anything, unless it turns out you were supposed to do it, in which case for the love of God, don't not do it!
Fry: Got it.
Professor Farnsworth: If, for example, you were to kill your grandfather, you would cease to exist.
Fry: But existing is basically all I do!
--Futurama episode "Roswell that Ends Well" (TV 4x1). A joke that only works if you allow paradoxes.
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