What Effect Does Sun Exposure Have on Melasma?

While on vacation at my in laws beach house in North Carolina and also while in Antigua I noticed I was getting brown patches that looked like a mustache above my upper lip. When I got home it slowly faded, even after I had continued to be in the sun (I do always use sunblock). This year we went back to Antigua and the brown patches increased and seemed darker. I went to a dermotologist and found out I have Melasma caused by birth control pills. I have stopped using the pills and have been using a lightening cream. It is summer and I miss being able to go to the beach or outside for a gathering with friends. The doctor told me to stay out of the sun or it would return. I live in NY and have never seen the mustache appearance here- only when I was in Antigua and NC. Does the stronger sun there affect Melasma more or would it appear again if I was in the sun in NY? Thanks so much for your help and advice!