Am I just being silly, or is something going on?

i suspect my girlfriend may be cheating but i'm not sure how to tell, i get my suspicions from the fact she's cheated on a few of her previous partners before. i asked her for her password for a website we both use to message people, she says she didn't remember and was really trying to avoid the question. so i rang her up before and got quite mad asking for the password because i'm really worried she is hiding something on there, literally as soon as i called for the question she just moaned about how she wanted to sleep, i love her more than anything but i'm not sure i should stick around because i feel like she really doesn't care at all. she has acused me of cheating in the past and i got pretty mad about the constant nagging because i really wasnt, maybe she feels the same way? i don't think she is meeting someone in person because we spent most of our time together, but i am worried something is happening online that i don't know about, i get upset over this a lot of the time and i am not sure what to do