Do you owe your spouse sex?

I'm 12 weeks pregnant and never seem to be feeling well. I'm always nauseous and have a headache and when I get too warm I throw up. It's been pretty bad. So bad that I cringe at the thought of sex. That's movement and getting warm two things that have been bothering me since about 5-6 weeks. My husband has been rather harsh on me about us not having sex when he wants and I try to explain that I just never feel good and my libido is super low right now. I really can't help it. So I apologize over and over. He asks for sex non stop and then throws a fit like a child when I say no. I mean slamming doors and raising his voice at me. I really have tried everything. Even on nausea medication and stuff for my headaches I still feel awful. So my question is...do I owe my spouse sex when I feel this way? Is it all right for me to say no. I'm actually crying because he makes me feel so shitty about it and I just can't help the way my body feels.