My 2 yr olds cut looks infected?

Yesterday my son cut his lip it was pretty bad but we didn't go to the doctor. I put hydrogen peroxide on it twice yesterday but this morning it looks like it might have some puss which means it's infected. Should I take him to the doc right away? Or should I keep putting peroxide on it?
Update: It's on the inside of his lip you cannot see it. My doctor told me he seemed fine over the phone yesterday. put peroxide on a q-tip and dabbed it on his cut. My question is if you child had an infected cut would you just keep cleaning it or take him to the doctor?
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