I've had a rough couple of days. My son has been sick (hives everywhere, apparently allergic to amoxicillin) so he's been home from school, and since I'm on disability right now I've skipped partial to stay home with him. By the end of the day I have been supremely frustrated.
That sounds perfectly normal for anyone sick who is in turn trying to look after someone else who is sick.

My son (he's four) has been going through a rough time right now, to the point that his teacher has suggested I take him to be evaluated by a psychologist. Some of his behaviors are tantrums in which he ends up hitting himself on the head hard when he doesn't get his way, hitting other children, not listening to anything I ask him to do, and not eating the food he asks for and just eating junk food. I know that tantrums are normal but it's not normal for him to hit himself in the face and head.
Your sons behavior is not your fault. It appears that he needs specialized help and you recognize and are no doubt doing something about that. Well done.

And the fact that he doesn't listen unless I yell at him is very frustrating. I have to ask him six or seven times to do something before he acquiesces and I end up yelling at him to get him to listen.
That would and does frustrate every parent. Doesn't make you a bad parent because you get frustrated.

I feel like a terrible mother. I feel like everyone can see what he's doing and is judging me for it.
Let them. How many times have you seen a child throw a tantrum in the supermarket? It happens. Your son loves you and wants nothing else but to be with you, sick or not.

He also has two cavities in his two front teeth which I don't understand because we've always brushed his teeth every night. I know I should in the morning too but I forget. I forget lots of things. Anyway I feel like every time someone sees his teeth they're judging me.
Again, your doing something about it, not ignoring it. That makes you a loving and caring parent.

I'm scared that I'm screwing him up.
Every parent has that thought!!

I've been hospitalized six times in the past two years and every time I'm gone I can't see him bc they don't allow children on the ward I go to. So he doesn't know where I am and he doesn't know I'm ok. My sister in law told me that the last time I was in and she babysat he told her "it's scary when mommy's away". How awful. What am I doing to him?
You are trying your best. Every parent gets sick at one time or another. Not all have to go to hospital, but alot do. All your son wants is to see you and be with you. How can that be a sign of a bad parent.

I guess it's worse because my mom was sick with depression. She didn't get hospitalized (one time) but she basically neglected me for my whole childhood.
Do you blame your mum for having depression, or for letting that depression lead her to neglecting you? It sounds like the latter....

I don't want to do that. I don't want to get so frustrated and angry with my son. I've grabbed him and squeezed his arm really hard. Isn't that abuse? I'm so ashamed for how I've acted these past two years while this illness has run rampant.
This is something that it would be really good to talk to a T about. You already recognize that there is something you want to change about yourself. A Therapist can help you with that.

The only good thing is that things are finally stabilizing. It's only been three weeks so I don't know if it will last but things are definitely much better now. I have to focus on showing my son I love him no matter what.

I know everyone's going to say I'm not terrible but can you just give me legitimate reasons why? I can't see any.