OP, this isn't alright. He tries to sexually assault you and uses emotional blackmail to try and get you to have sex with him, then accuses you of lying to 'get out' of sex.
Your wording is sad, too - "turn him down". Do you see sex as something he does and you just accept, or has he made you feel that way? Do you ever get to decide when you have sex, on your terms?
He is not a good man. From this page: www.loveisrespect.org/resources/types-of-abuse/
Under signs of emotional abuse:
Making you feel guilty or immature when you don’t consent to sexual activity.
Gaslighting you by pretending not to understand or refusing to listen to you; questioning your recollection of facts, events, or sources; trivializing your needs or feelings; or denying previous statements or promises. (I'd argue accusing you of lying about headaches falls under this, plus the physical abuse trivialises your feelings as well as being physical abuse in itself)
Under sexual abuse:
Unwanted kissing or touching.
"Threatening, pressuring or otherwise forcing someone to have sex or perform sexual acts.
Please leave. You deserve better, I promise.