Am I in an abusive relationship??

I moved into my partners house 2 years ago which meant I had to give all of my household furniture away. I noticed after I moved in he started being very nasty to me. He would grab my legs and say "thunder thighs" would make sexual comments about other women in the street or on tv, would tell me to lose weight and basically just put me down and insult me. I hoped it was just some sort of phase and 7 months ago we bought a house together and moved in. Since we moved in he has gotten worse and worse. The insults have gotten worse, he picks on everything I do, moans when I make plans with my family, he's drinking has escalated but he doesn't see a problem, he has left slimming world leaflets out for me (I'm a size 12/14) he tells me I should do a workout because he wants me "fit not fat" says he doesn't want me "waddling down the beach" he also seems to be getting more violent but I don't know if the things he does would be classed as violent? Last week he was standing behind me, screwed his shirt up and threw it, it just missed my head. He was angry because I didn't want to have sex with him, the most worrying thing is when a few days ago he started groping at me so I pushed him away and he put he's hand on my throat, he didn't squeeze or anything like that but it did shock me. I told him to never put he's hand on my throat again and he said "I should throttle you" I don't know what to do and I really need some advise. I'm now stuck with this house with him with no where to go. I have looked into private renting but it's so expensive and I would have to start from scratch and but absolutely everything but with little money, I also have 2 cats and most landlords won't allow pets. People tell me to give them up but they are all I have left. Can anyone give me some advise? He says I'm being stupid when I get upset at he's nasty comment ect, am I??