Can you get sick from a sunburn?

Yes in severe cases: Sunburn if severe can cause a systemic reaction which can lead to an acute illness such as feverish feeling, dehydration, and fainting. It is important to stay well hydrated, treat the skin blisters if any and the burn on the skin. Visit a doctor or emergency room if you begin to feel light-headed, nauseated, or begin having severe chills.

Infections: In addition to excellent info provided by dr. Patt if blisters open they are more vulnerable to infection. Pus, redness, swelling or increased pain likely mean you have an infection. In the meantime, aloe vera can help with sunburns.