You're right about being exposed to the sun. "so much time" does not have a clear meaning in your sentence. You could just say "for some time".

It can mean "to be positioned or oriented in so as to receive sunlight." "Our south windows catch the sun on winter afternoons." "He was momentarily dazzled when the rear window of the car ahead of him caught the sun." "Don't plant those flowers over there, they won't catch enough sun." It can also mean "to go into the sunlight," as in "I want to catch some sun today, I think I'll take a walk now." In the United States, informally, suntanners will say "I want to catch some rays."

it is hard to give an accurate answer when something is not in context - however, I am familiar with that expression to mean that someone has got a little bit sunburnt. "You have caught a bit of sun". There may be other meanings - context really is everything!