Before you make a decision, please read what others have gone through, how long that they had to work to salvage a relationship after infidelity. People on infidelity subs will tell you it will take 2-5 years to recover. Also, the relationship you thought you had, no longer exists - it is gone forever. One of the subs is r/survivinginfidelity there are others as well.
It is a lot easier for others to give advice than it will be for you to implement it. We can all tell you what you already know in your head but that is not necessarily what rules us. We are not invested in your relationship like you are.
I will share a story from my past: I was in love with this woman when we were both 23-24 (it was the first time I felt that way). I had placed her on a pedestal, she was perfect in my mind. I was in college and a couple nights before one of my finals she decides to go out with this new guy who she said was a friend (we had been dating over a year at this point). I knew better, because I saw the way that they would interact (had I been more emotionally mature, I would have probably walked away earlier). She told me that they were going to hang out all night and watch the rain or something like that. He was going to stay at her place and I was told to leave. Obviously, they were more than friends. I knew it, I just could not emotionally accept it. It crushed me. It was cruel.
I tried to work through it, tried to move forward, tried to deny anything was going on. It changed me for the worse. I do not like who I was after this incident until the relationship ended (I logically knew this - I could not emotionally handle it). While I don't have too many good things to say about by ex-girlfriend, she did one huge favor for me: She dumped me. For a while it was insult to injury. It hurt, it was embarrassing. Male ego destroyed so to speak. This was 25+ years ago. I can now look at that time and laugh. I thank God that I did not waste more time with her. She taught me something important - when someone treats you less than you deserve it is incumbent upon you to change that. If that means to take the loss, feel an incredible amount of pain now but know that in time you will be stronger and happier. When you are mistreated by someone who claims they love you, you will know better how to react and how to move forward - and move on.
Most people who have dated more than a few people in their lives have been cheated on, whether they know it or not. I used to think that people would judge me for being cheated on but now I realize that is such a fucked up mindset. As you get older you realize that those who cheat are the ones to be judged.
I really wish I could tell you that I immediately fell in love with someone new after getting cheated on and dumped, but I didn't, not for a few years. I had to date a few more women (most of whom were great people, but alas we were not great together). What I was able to do was to become best friends with two amazing guys. We grew up together and had an amazing time and still consider them my best friends even though we no longer live near each other. 3 years or so later, I met my wife. She thought I was a complete ass at first. We then started to hang out. Then started to date. For the past 23 years we have been together (Our 20th is in November). We have seen or spoken to each other every day since we started dating. We have had some great times and some tough times. But through it all, I am in love with her and she is in love with me. Because of that experience many years ago, I have lived my life in a way that I would not put myself in a position where I could be questioned in terms of infidelity. While I have never asked her experience prior to me (and nor do I want to know) she has never put herself in a position where I could question her faithfulness.
You are young. You are in the prime of your life. Please go out and experience it. Seriously, a 22 year old woman has so many options when it comes to dating, I cannot image why you would stay. As a 22 year old - you have opportunities of meeting some amazing people. The unknown is scary, but that is what makes life exciting.
Return question for you: You indicated that you were both in a bad place in February. Even though you were in a bad mental place, did you cheat? No. Do you really even buy his excuse? What will his excuse be the next time? Or the time after that?
I would also like to point out that he did not come clean until he was outed by the other woman. He had no intention of telling you. He had no intentions in being a better person until he was caught. He is not changing to better himself - he is doing it to placate you into staying. It wont last
Also, do you want to have to deal with a gambling addict? That alone would cause me to walk. While I don't believe in gambling, I'll bet you 20 dollars that his changes are only short-term and he will go back to normal the moment he thinks he can. In fact I will give you three to one odds on this, no wait, five to one that he will learn he can blame cheating on being in a bad place and will be forgiven. (Sorry for the movie reference). I suspect he has blamed prior bad behavior on being in a bad place. BTW, it is not an excuse, it does not justify it. It is simply shitty behavior.
You deserve so much more than to be treated this way.