wow, wow, wow. First of all, only a super insecure person would ever tell you something like that. Maybe he is the one doing the actual cheating if he has that mindset.
What you did was OKAY. Are you not human? It was stupid, maybe wrong, but it's normal for a person to do something like this when they feel the need for validation. Most people live this way their whole lives. You did the most important step - admitting how you feel and trying to do something about it. The next step is to accept it. Thing like this happen. Even if you slept with someone it wouldn't have been the end of the world. It is sex we are talking about, a physical need we all have even if we are in a happy relationship with our "soulmate."
This is why some of the happiest people are in open relationships, but I won't go deep into that because most folks have no idea what an open relationship is. However, your problem is not the desire for sex, it's a mental issue.
Do not tell your boyfriend, he doesn't seem like a person who would even try to listen to you, he might act without thinking and break up with you and then go around telling everyone you're a slut Yet again, why would that matter for you if you're not together. Why would it matter what his parents think? What would they say if you tell them he is not man enough to keep your private life away from everyone's ears.
I believe you can deal with this problem by yourself at first and only if you truly think telling him is the right thing to do, you can say it. But ask yourself if you want to do it because of honesty, or because of your own guilt and subconscious need to break up with him.
Lastly, you are too young. What reputation do you have? Are you an Instagram influencer? Do people look up to you? No, they don't. Do you know how many times I've ruined my "reputation" at school and university? Do you know how many of my friends were labeled sluts? It didn't matter one bit. Life goes on. It will all be forgotten the next day. You will think of this a year from now wondering how you could have made such a big deal out of it.
Ask yourself if you love your boyfriend and do you want to be with him for the next 3 years?