Is it normal for my girlfriend to act this way?

I do get jealous sometimes of my guy having female friends but I do try to deal with it. cause me and him love each other

Some jealousy is normal. And if a guy has a lot of female friends, I think some conflict is inevitable. Getting mad at hugging a friend is not normal and probably indicates insecurity, lack of trust, or both.

Some people don't embrace anyone but their family. Artists and musicians (saw your profile) tend to be a little more liberal and into the shows of affection for friends, so if she is more straight-laced, I can see how it bugs her that you hug your female friends.