Is this considered rape?

It sounds like rape to me. They should listen when you say you don't want to, not try to persuade (especially multiple times), and also stop when you no longer want to. And drunk people are even more vulnerable so they deserve more caution.

From what I read it is rape.

Yes, you were raped. Even if you were manipulated and bullied into agreeing to sex at the start, the moment you said you wanted to stop and the asshole kept going, it became penetrative sex without consent. That is the definition of rape.

As the father of a daughter, I found reading your story traumatic. I can offer you no advice on how you come to terms with the rape, but I know that there are support groups available in many places where women who have been through similar things try to help other women deal with the consequences.

Contrary to what one of IIN's resident idiot trolls has posted here, everyone has the right to withdraw consent to every sort of sexual contact at any point. If that happens, then it changes the moral and legal situation completely.

It seems to me that an important question you should be asking yourself is why you find it so difficult to accept that it was rape. Maybe you grew up being told that only women of a particular sort ever got raped, and since you don't consider yourself one of "those" women, you resolve the cognitive dissonance by reclassifying what happened to you? Maybe it's difficult for you to accept how you had no control when he was doing what he did? Maybe you wonder if, deep down, you wanted it, because you (like a lot of women) have fantasised about being forced to have sex? Maybe you've thought about what you'd do if you were ever raped and you imagined you'd be a strong woman, but in the event, you found the situation so difficult to deal with that you actually just collapsed in a helpless heap? Or maybe you blame yourself for what happened because you chose to drink until you were at least borderline incapacitated and your inhibitions and judgement were severely impaired?

If it's the last, then I have to say that I think there's some truth in that. Men should stop when women say "no", but everyone with any sense and a degree of maturity should understand that getting shitfaced rarely leads to anything positive. I do understand that in some environments there's a lot of peer-pressure on young people to regularly get plastered, but you need to understand that there are a lot of scumbag guys around who will eagerly take advantage of women who are incapable of rational thought and physically incapacitated to some degree. It's shitty that that's how the world is, but those are the facts.

Finally, while I know you were the victim here and it's seen as horrible these days to place any responsibility for negative consequences on victims, I do strongly suggest that you have a long, sober look at your alcohol consumption habits. If you're in an environment where getting drunk is seen as normal or even necessary in order to have fun, you might consider working on developing the self-confidence that will allow you to refuse to drink at all, or at least decline further drinks when you know any more would be unwise. Tell people you're on a diet (have you ever looked at the calories in alcoholic drinks?). Tell people you're doing some weird detox thing. Tell people your father died of alcoholism or something even more dramatic. However you do it, either take responsibility for drinking in extreme moderation (or not at all), or learn to accept that you'll probably have further alcohol-related problems in the future.

Hoe, even though all da niggas in da hood send our condolences, da one thing yo ass forgot is that there's no take backsies!
You can't just tell a nigga he can have sex witchu and then change yo mind in da middle of it. You don't build a bridge and decide to stop halfway. You want people to die, bitch?!
Walk it off!