I had just complimented my cousin on her hair when my mom told me that my cousin's mom was very upset because her daughter's hair was falling out. I was shocked and it seemed weird. What would you call this situation? Ironic?
Your comment was a "gaffe"
gaffe (noun) - a social or diplomatic blunder. "He realized that he had committed an awful" gaffe when he mispronounced her name.
and the situation was "embarrassing"
embarrassing (adj) - causing to feel shame or chagrin or vexation
It sounds to me as though it was just an unfortunate remark, ( though unless the cousin, him or herself, was upset, I can't think it will matter in the least). It couldn't be helped in any way, was no one's fault, and is most easily rectified on the basis of 'least said - soonest mended'.