How long has this been happening?
It could be herpes - some people describe their sores as looking like paper cuts. They would definitely burn when you wash or wipe. Do they burn when urine hits them, too?
Have you seen a doctor? That's a must. Even if it isn't herpes, it for sure sounds like something that needs to be checked out. It could be an allergic reaction to something, or a variety of other things, but get to a doctor today if you can.
If they think it's herpes, make sure they do a type specific culture or PCR swab on it. They may say it's too late to do it, if the sores have started to heal, but ask them to do it anyway. If it comes back negative, you can get a type specific IgG blood test later. Don't let them do an IgM herpes blood test. It's unreliable and shouldn't be done on anyone but newborns.
Let us know what happens.