I don't think you have sunburn! I first experienced the same thing about two years ago. I thought it was sunburn, so I tried all kinds of lip balm with SPF. It seemed to get worse, much worse! It was horrible, I looked terrible, like a clown, and refused to leave the house. It took months to figure out, but apparently I have an allergy to some ingredient found in almost all sunscreens. Since I have used sunscreen all my life, I'm wondering if some new ingredient has been added recently.
Yesterday my sister-in-law used regular sunscreen, and then played with my kids. Enough transferred onto them, that I got a reaction by hugging and touching them later! The only kind of sunblock I can use on myself or my children is very natural stuff with Zinc oxide. Unfortunately, it is not very waterproof, and is very visible (a white cream) when first applied.
If anyone knows anything more about this kind of reaction, please let me know!