No. Do not pick at it, as that could cause an infection. Nurses are trained to remove dead skin to facilitate healing, but they use a sterile procedure. Please see a doctor. An infected burn is a terrible thing to have.
If the burn is simple then you can remove the dead skin.It will drop itself as days go on.So you need not worry.But apply medicine on it.If the wound is due to chemical burn then get the doctor's advice.If you remove the skin,be carfull.After the removal apply ointment to avoid any infection.
You should leave it alone if you can. If you know it is too tempting to try to pick at the burn, then put a band-aid on it. If you have Neosporin use that as well.