Both Staci and Dorothée are right. :) "I've been married for about three months" is the most common way to say this, and "I got married about three months ago" is fine, too. You can't use the present tense "am married" if you're describing a span of three months. You need to say "have been married" (to show that the marriage started in the past and is still continuing), or just use the past tense "got married" (to describe the event of getting married, which happened in the past, and is finished).

#2 is the correct version

Thanks Robert, Dorothée, Gray.

# 2 is correct, # 1 is not good English. You could also say, I have been married for 3 months

You could understand the sentence in #1 but it's not grammatically correct.