I'm sorry about all the pain you're going through. I wish you could show your dad the letter you wrote this site, so he would see what a selfish and irresponsible jerk he's being - not only to his poor wife but also to his daughter to give her all these health problems.
I really think you need to let it all out; you need to talk to someone who'll listen. They usually have counselors at school who'll keep everything confidential. If not, you need to find a counsellor and go. Tell your mom you need to see someone.
Also, write your dad a letter like the one you sent and explain how bad you're feeling. If there are any family friends who can help yr mom and dad and who know about their history, you can turn to them for help.
Yr boyfriend obviously cares about you but there's not much he can do except be there for you.
It must be hard worrying about yr mom& dad but yr not responsible for what happens between them. If your mom puts up with wrong behaviour because she's drained, she may eventually get sick of yr dad and kick him out. But he's still remain yr dad- and you'd still have contact with him& get to see him.
Kids always worry about divorce but it's not the worse that can happen. As much as possible, you need to distance yourself from the negative atmosphere in your house. It's not healthy. You need to get busy with yr school, go out with yr friends, have your own hobbies; don't spend too much time with your family if it's going to make you feel sick physically.
You have to be sure to eat well and go to a doctor; taking care of yourself is important. Your mom will be worried about you too- and it will only add to her worries. You can spend time with yr mom& try to make her feel better but don't take on her worries; it's more than you can or should have to shoulder.
Be nice to your boyfriend. Tell him that yr sad things are so bad at home, and want a shoulder to cry on. It's good he's there to support you emotionally; give your mom& other friends a chance to be there too.
The first thing you must do though is go to a counsellor and talk about all yr feelings and fears. Write yr dad a letter explaining calmly how you feel and how sad you are. Then give him time to come to you. If he doesn't respond, ignore him, give him space, and spend yr time with friends and your mom. But get out with friends and busy yourself with your hobbies. And study so you do well at school. Try to exercise and walk and look after your physical health. Getting sick won't help anybody.
You need to be strong. Have faith that things will work out for the better; if your parents divorce, it's not the worst that can happen; I know that's what you fear. But it would probably be a blessing in disguise. Because your dad would not live with you and the atmosphere in yr home would be better and less strained. But yr dad would visit you and have contact with you. Your mom will be in pain for a long time (whatever yr dad does) but it might be better for her in the long run if he goes, given that he won't change his behaviour. She will need your support and her friends' and family to help get her through this tough time.
Pls don't wait any longer. Talk to a counselor today, write yr dad a letter then step back & see what happens, tell yr boyfriend& friends how you feel, so they can all support you. And live your own life (school, friends, hobby) as much as you can, so you're distanced from the negative stuff at home as much as possible.
Good luck and I hope things get better.