Are there any low-cost health clinics where you live? Any psychiatrists or counselors who will see you on a sliding scale? Does your college/university have a counseling department? Can you get student insurance through your college/university? I realize that, when you're stressed to the max, the last thing you want to do is research these sorts of options, but perhaps one or several of them might help you.
I agree completely with GreenTeaHero: Don't let your father talk you out of taking your meds! You are, as you say, 18, after all, and an adult, and able to make these decisions yourself. If your dad won't keep you on his insurance, please do check out some of my suggestions.
I wish I knew about whether going to the emergency room would get you your meds. It might be worth calling them and asking. If you just turn up there, I'd be concerned that they'd deem you a "psychiatric emergency" and try to institutionalize you. Of course, you'd have to be, at least under the laws of my state, a danger to yourself or others to be involuntarily committed, but I'd hate you to take the chance. Call first, just in case.
My heart goes out to you. Take good care of yourself. And as so many others have said, stop, and breathe. Sometimes, again, as others have said, it's about the only thing we can do.
I know we'll all be thinking of you.
Warmly and with sympathy,
bipolar II, fibromyalgia, chronic fatigue syndrome
current meds: Invega, 1.5 mg; Clonazepam, 0.5 mg prn; Lexapro, 5 mg; Mirapex, 2.5 mg; Topamax, 50 mg