In a relationship you should work to tackle a problem together, and not try to take eachother down.
It sounds like he is concerned for you, and when the boy cried wolf no one came. If you were taken advantage of that is terrible, and I hope he had supported you at some point at least.
Look at this way, his gf/bf has a past of being a bit naughty, and now they admitted to being taken advantage of. That is where his mind probably jumped to, you cheated again because you have a history of it. His thought process isn't ridiculous at all and completely natural.
I think you need to discuss this with him, tell him what you said here (that you really were taken advantage of, and realise how suspicious it looks given your past but all you ask for is support and understanding) and maybe devise a plan to not let this happen again. Maybe making sure you always have a friend? Reporting the person? Trying to limit your drinks (which both me and my bf do to avoid such situations)? The world isn't rainbows and unicorns, and there are terrible people out there who want to hurt you and will; you really need to take care of yourself.
Second of all, you acknowledge you have money problem albeit not a huge one. This seems to be coming from.a place of concern (although I don't know him enough to say 100%) and I think you should hear him out. Ask him why it is such an issue to you two, you need to hear out his concerns even if you don't see the problem (often with bad habits we don't, and we need someone from the outside to let us know). Remember to explain why you don't see the issue, but don't let it get to an argument; compromise somehow.
Regarding your last point, again he is just concerned. Why would he say that to tease you? And if he wanted to leave you, why does he even care you 'cheated'? Try and put yourself in his shoes, or maybe speak to him about the concerns he has and let him vent and make sure to listen. I think it would be wise to see a doctor if you even have a thought in the back of your head that he may be right on this one.
Don't let these anxious thoughts about him breaking up with you get the best of you, cause they will and you will end up breaking up. Speak to him. Tell him how you feel, don't be afraid if you think it will hurt him because you two deserve to fix these problems together and you can't leave anything behind. .