I was with my partner for 7 years and have a 5 year old daughter! Over the past 3 years I have been trying for another child, but nothing seems to be happening. We have split up now, but I am worried that something could be wrong with my fertility. Am I able to have this problem checked out without having a partner?:(

I'm not so sure what you mean by your last line "have this problem checked out without having a partner..."

You can simply go to a fertility clinic and have yourself checked out.