I assume you saw a doctor, because you know it's a second degree burn. If you've handled the infection part, get an aloe plant and use the gel on it. This should help speed healing. And as suggested above, you probably need to cover it to keep dirt and bacteria out of it.
Can you get it looked at as it will need some treatment ,a band aid put on tightly or maybe a butterfly clip may do with with an anti biotic cream if you cannot get to a doctor .in my opinion a professional to treat it would be better .good luck