‘I haven’t gotten married’ could mean ‘I’ve never been married.’ Or ‘I’ve always been single.’ You could also say ‘I’m in a common law marriage but I haven’t gotten married. ‘ ‘I didn’t get married.’ Is talking about a specific time in the past. I proposed and she accepted but we didn’t get married. (Or just ‘we didn’t marry.’) My sisters married right out of high school but I didn’t get married until I was 35.

I'm not married/I'm single.