If you are read as female by people I could see how they would think you are angry with your neutral expression.
But! When read as male - I don't think they would think that as much. Your face is actually very male, not angry. It is your cheek bones I think. Once your hair is cut short, at least from this picture, I think your face will pass really well. Your glasses are great for your face.
Now, for a haircut - something simple and short, but not buzzed. I am not good with clipper lengths, but maybe someone on here will stop by and tell you what clipper length you should ask for on the sides and the top. Then, you could just go somewhere, tell them the lengths, and have it be done.