You're horse doesn't know that you're on your period and feeling bad. So beating him up when you are irritable is simply going to teach your horse to be wary of you. He won't trust you under saddle or on the ground if this continues. Would you beat a child because you were in a bad mood?
Go to the doctor and talk about options for going on the pill. It was the best thing I ever did, I used to get terrible PMS, to the point that I would take days off work because I knew that I would probably mouth off at someone and lose my job, without intending to. Since going on the pill, I've been absolutely fine and moods are totally stable.
Another point to note, is that if you're having a bad day or feeling simply short tempered, feed your horse, give him a pat, and go home again. It's going to be far more productive for the horse to spend an extra day mooching around the paddock, than getting worked and fighting for an hour. You will then both come back feeling even worse than when you started.
Don't take your moods out on your horse, there is no excuse for that.