I(F25)am seeing another guy that's not my partner (M28). How do I stop?

I(F25) have been in a happy relationship with my partner (M27) for 9 years. We have been together since our teenage years. He was my first love, first kiss and first everything. I never looked at other men, never even thought about it until recently. Now please keep in mind that my relationship is very healthy, well at least it was until I decided to screw up. My partner is very caring, loving and he really is the best boyfriend anyone could ever ask for. I was set on marrying him. Well recently, someone (M28) messaged me on social media and I wasn't even planning on opening the message but it was a question for my business so I replied. It was a smooth talk that soon led to another conversations. At first the conversations were friendly and normal, I even told my partner about it. But then the conversations started getting more romantic, he was complimenting me ect. He is also in a relationship of 2 years. I knew he was a cheater and a plyer so I didn't give it much thought. Well he asked me out and I really don't know why but I agreed. Basically he picked me up with his car and we just talked and drank coffee. He tried to kiss me but I didn't let him. When I got home I felt disgusted with myself and I regretted going out with him. But, I didn't cut contact. We continued messaging each other and we ended up going out again. This time I actually made out with him. He tried to sleep with him but I refused because guilt was eating me up. So we continue messaging each other. This is where it gets worse. I even start thinking of him when I have intercourse with my partner. I feel like the biggest piece of shit to ever exist. So you'd think I'd stop? No. I go out with the guy third time. Again, we don't have sex but this is still cheating. We were talking and he confessed how he thought we would only have sex and then never see each other but it turned out to be something deeper than that because he knew I would not sleep with him but he keeps wanting to see me and reply to my messages and how he feels at peace when he's with me. I realize we both sort of share the same problem. I really know I should have not done this. I should have stopped. I shouldn't have gone out with him nor replied. So I am here questioning my every single moral that I thought I had, but I guess I don't. I ask myself even if I love my partner and somehow I think yes. But why would I do this if I did? The sane thing is to break up or at least come clean to my partner, he does not deserve this. I want to say that I don't want to lose him but my actions won't match my words. The thing is even If I leave my partner for this new guy, we would never work out. On the other hand if I stay with my partner at least I should come clean right? I am a coward. And I really can't stop thinking about this new guy, even when I sleep, I dream of him and when I am half awake I think of him. I am not sure if this is love. I can't even pray to God because I am ashamed. I know I should stop but I can't. I am a shitty person with no morals, you are all welcome to judge me or even call me names but I just feel so confused and so lost right now. I can't talk to anyone about this. So please tell me how do I proceed?