See your doc. This is not normal and should be evaluated by a medical person. The longer this condition persists the greater the chance of permanent damage to the nerve.
Numb fingers. There are several possibilities. One is that you may have peripheral neuropathy. Call your doctor for an appointment for an examination to determine the cause.
Cool, not cold. Water followed by more cool water, clean dressing and Naproxen or Ibuprofen for pain. If still severe contact your doctor then go buy some oven mitts.
Ice the burn. The thing to do for any burn, immediately, is to grab a pack of frozen vegetables or an ice pack or ice in a baggie and apply it for 15 minutes to the burned area. This will reduce the pain, limit the spread of the burn, and be of great relief. If you did not do these, or applied oil or butter (useless!), then you will have a painful area to deal with. Protect it, keep it clean and wait.