I've been to the beach before and this didn't happen. I've noticed that putting ice on my face helps a little. If you use the sun block only on your face and you notice this reaction when you are in the sun, it could be a reaction to the sun block. If you use it anywhere else on your body and do not notice redness or a rash, it probably is not a reaction to the sun block. Certain medications can make you more sensitive to the sun and more likely to have an intense sunburn.
People can also be allergic to the sun.
Be very careful about how much sun exposure you get and seek the advice of a dermatologist if it continues. Check the calendar.