Do you think you can have MRSA and not know it?

Yes. You can be a carrier, and without an active lesion, or sore, you can have it and spread it. You can treat it by using bactroban, (mupirocin) or Mupirocin ointment.
Sure! Staph skin infections though will fail to heal, and you should seek advice asap for any non healing skin lesion or rash.