Kitten bit me! :(

[Savvy_Darling]

My 2 month old kitten was playing with my arm and bit me. I'm wearing a long sleeve soft fleece shirt but it still really hurt. I pulled my sleeve up and there were little puncture marks.. no blood though. Of course I hurried to the bathroom and put peroxide on it and then washed it with soap and water and then more peroxide and then apple cider vinegar (good for cuts) and then again more peroxide..I even rubbed some hand sanitizer on it since I didn't have rubbing alcohol. After all that I put some manuka honey ointment for infections on it and then slapped a bandaid on it.
My kitten has had all shots except rabies since she's only near 3 monthes old and has only been inside. Only thing is that she might have had a cold and I've been giving her medicine for the past week but she's been acting perfectly fine and like a normal healthy kitten. I'm scared I'm going to get some horrible infection that's gonna kill me or make me sick or just something just awful.
My anxiety is doing a number on me and I'm so scared. I have refused to Google anything but I know I've heard of cat bites causing infections before. So again I'm totally freaking out. I keep wondering if I cleaned it good enough or if I should do it more. The bite is on my upper arm and again no blood was drawn just little puncture marks .. and I am wearing a long sleeve extra soft fleece shirt.
I just need some opinions on this! I'm bugging out ;(