paresthesia, is I believe what this is called. Disclaimer: take everything I say with a massive pinch of salt, I am no doctor.
my husband has a known neurological condition and often get's the "invisible sunburn" (as he calls it) it can be very painful, and I don't think I'd be letting my GP give me the brush-off.
this is only wiki, so not brilliant, but if you skip the first few paragraphs (which refer to this in it's simplest form, pins and needles) then the later bit might help you somewhat.
en.wikipedia.org/wiki/Paresthesia
it can be caused by something as simple as shingles or a cold sore at the "tingling" stage (which you have none of the other symptoms of), but it can point to other more sinister things. Please don't let your GP brush you off. I have seen my husband reduced to tears because of this, and nothing I have tried to ease his pain helps at all (calamine lotion, after sun, menthol talc, ice packs, cold compresses, pain killers etc)
one year on holiday he fell asleep on the beach, legs sticking out under the parasol, he badly burned his shins, they were blistered and peeled for weeks. According to him that level of proper sunburn is exactly as painful as his invisible sunburn, and I really don't think it's fair of a GP to just brush someone off with that level of pain and discomfort. And that is aside from the fact as it could be neurological, it might be very important to find out why you're getting these symptoms.
Google paresthesia on more reputable websites than wiki, and if need be do some print outs and take them with you to your GP.