I'm curious, you say, ''I've met guys and had sex with them but it's never gone beyond that and its usually left me heartbroken''. That tells me you could come across as clingy, being heartbroken after just meeting them and having had sex.
Anyway, I don't agree with 'joining a club', not unless it is a dating club/agency. A club is the typical answer given by Agony Aunts or Americans ('join your local church'). Joining a club simply to meet men will leave you disappointed because it is likely the men are there to do things related to the club. Their intentions will be different to yours.
I did do dating sites after I was divorced. Met some good ones and bad ones, but that's life.
Relationships just happen sometimes. I've had one night stands. Some never went further, a couple of others lasted 4 years plus. In my experience though, I would say that one night stands or having sex at the first opportunity come across bad for both the man and woman. It gives a perception that they can't be trusted in a relationship if sex is so forthcoming that quickly.
I went out with a woman who said she had sex with a non league football team in a hotel over a weekend, her friends confirmed it was true. I ran a mile. I know it's an extreme example but one that may give an indication as to why men go no further with you.
I would try dating sites. My Uncle has just met a lovely woman, they are both in their 70's. My best female mate is marrying a guy she met online 4 years ago. Dating sites used to have a reputation of being for sad people, these days plenty use them young and old. The better ones allow you to put info about you and allow your personality to come across. That is a better option than meeting someone at a club or a pub when you are both tanked up and can't wait to get into bed.