First of all congrats on your new tattoo! What did you end up getting?
Second, friction can affect a tattoo overtime. That's why things like finger, palm, and sometimes ankle can feet tattoo are prone to fading much more quickly. There will be a lot of things that can cause your tattoo to fade, and no matter what it will fade with age. I don't think the arm sleeve would hurt it any more, but I wouldn't obsess with it too much. Just take care of it, keep it and your self hydrated and moisturized, and remember you can always get it touched up in the years to come!
So I recently got a tattoo on my inner right forearm, and I am a pretty big PC gamer, playing many hours a day. I tend to drag my arm over my mouse pad for mouse movements, and am worried about how it will affect my tattoo? Should I worry? I am thinking of buying an arm sleeve later on when my tattoo fully heals to prevent the direct contact between the tattoo and mousepad. If you have any suggestions, please let me know.