Should I stay with him?

So my boyfriend of 1 year and months cheated on me a about 2 weeks ago when I was on holiday . It was just a kiss but he said she was also dancing on top of him and he had his hands all over her , which obviously I’m really upset about. Before telling me he made up that he was really stressed about upcoming exams and that we should go on a break ( to try hide the fact that he cheated from me ) . It was all out of nowhere and I was confused so I asked him if he did cheat and he said no multiple times . Then he texted me later that day and confessed . Of course my holiday was ruined but we decided to talk when I got home which was a week after . A few people were telling me to give him a second chance which he was begging me to do and so I did . Last night me and him went out for drinks just the two of us and a girl in his college came up and didn’t even acknowledge that I was there and stood with her back to me and they were having a full blown conversation, my boyfriend glanced over to me a few times and I shook my head and mouthed stop to him and gave him a look the other times . He continued in the conversation , like asking her questions and stuff when she left of course I was annoyed but he didn’t seem to understand why . He said he knew I was uncomfortable ( but still didn’t end the conversation..?) . Am I wrong to be annoyed, I feel like he just prioritised her because he didn’t want to be rude to her , but he knew that i was uncomfortable ? Sorry it’s so long x