Cut The Mid Knuckle, Ran In Cold Water, Applied Neomycin, Swelling. Will The Skin Scar?

I just cut my middle knuckle on my middle finger this morning, little deep cut compared to a paper cut. Ran it under cold running water , rubbed it open to wash the cut, applied benzalkonion chloride towelette( it s all I had at the time) applied pressure to encourage the would to stop bleeding. Cut was still bleeding after I washed it and gauzed it up firm but not to tight, several hours later, took of bandage , wound closed right up, cleaned area and applied neomycin sulfate/ polymyxin b sulfate/ pramoxine HCL cream to it and left it to air out. Difficultly in bending it finger, still pain in middle knuckle and acute swelling to the area ( all this is on day one) With this description givin, what should I do to ensure that it will heal properly, and skin will not scar?