I've just put 'sin querer' into Google translate and it came up with 'unintentionally' or 'accidentally'. Both those sound much more natural to me in this context than 'without wanting to'. I've certainly heard people say that they 'accidentally fell asleep'.
'Without realising' is also something people say, although I think 'without meaning to' is more common in England. Certainly, it's what came to my mind when I first saw the Romanian sentence.
I have never heard any native speaker say 'without wanting to' or 'against my will' when talking about falling asleep. That said, the former would certainly be understood. The latter would also be understood, but might be seen as a odd for precisely the reasons that Alemehtais outlined. It could be interpreted as someone forcing it upon the person... like with a drug or something.