I think I might have an infection?

Okay, so I tried to jump a fence the day before yesterday, and I ended up getting a cut on my pinky which was about 2mm deep or so. I just put on some Polysporin, for infections, and pain relief, (even though it didn't hurt at all, other than when there was pressure applied to it, but most cuts hurt when pressure is applied to it)

I just did a little bit of research, and a common sign of infection is redness orpuffinesss. Around the cut, its a very light pink, and it is slightly puffed up. If I keep putting on the medicine for it, do you think it'll go away? And is it mild? Any information will be appreciated, and don't tell me to go to the doctor's 'cause I will.