Should I break up with him?

so my boyfriend can be really rude sometimes. i have some health problems and i went to the hospital yesterday and all he did was text me he didn't even come in even though he wasn't busy. i went home this morning and automatically he asked if i wanted to go out today. he knows I'm not feeling good. when we first met he said it was really easy for him to go out and hook up with other girls. he said if he thought i was lying he would. i told him just a n hour ago i didn't want to go out and he said "since you don't want to hang out with me I'm going to go hang out with someone else. i'll be occupied but ill just talk to you when your able to talk bye". i know he doesn't have a lot of friends and he NEVER hangs out with them at all. i think he might be cheating on me. or am i just paranoid. i know the one person he hangs out with a lot is a girl may they've been hooking up behind my back? should i leave him?
Should I break up with him?
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