I get jealous of almost over every little thing and I'm hurting my relationship because of it

HEADS UP! There is A LOT to read, I'll try to put a TLDR at the end if I can.

Me and my partner made a new friend (a transferee in our class) 2 weeks ago, and I've been getting jealous for almost every interaction my partner had with them. It really bothers me whenever I get jealous because I shouldn't be feeling that way, especially if all they're doing is giving each other a high five or a fist bump.

They have a lot in common, I'm pretty sure more than how much me and my partner have, and I'm worried that my partner will find them better than me. I get scared at the thought of them growing closer. I don't hate our friend, they're pretty nice and very outgoing, but honestly sometimes I wish we didn't meet them. You might be wondering why I even became friends with them, it's because I wanted to give things a chance.

Our friend added my partner on *** when they were looking for friends and saw my partner's *** on his bio so of course they added him. My partner told me immediately because he doesn't want to hide anything from me, even though he was honest to me and let me know immediately that someone wanted to befriend him, I got upset. My blood felt like it was boiling, all because of a silly friend request and a few messages. My partner recognized I was upset and he said that he wouldn't become friends with them or be close with them if I wasn't comfortable. But I felt it was too rude to tell my partner to not be friends with them, so I told him it was okay and that I'll be friends with the person too. But these past 2 weeks have been more bad than good.

This isn't the only time I've gotten jealous over little things, I got jealous with our other friends too. But I've made peace with those feelings, it's just happening again with our new friend and I'm sure I'll get over it soon but I don't know when and I'm scared I'll feel like this with every new person that comes into our life.

Whenever I get upset, I end up hurting someone. Whether it be me or someone close to me, in this case I've hurt my partner. It's not that I physically abuse him whenever I'm upset, it's jus that I've given him the silent treatment and acted distant towards him. But, one time when he was talking with them they were too close for my liking and after they talked I jus grabbed his arm and my nails dug into his skin, making him bleed a little. It was like an impulsive thingy but I deeply regret it because it's not his fault I feel this way. This jealousy issue or whatever I have is something wrong with me, he didn't do anything wrong but yet I'm hurting him because of how I feel.

My partner and I have talked about this and he said he didn't mind and that he could take it because it was better I was hurting him and not myself. We've been together for almost a year so he knows how I feel and how I get jealous over little things, and he tries to adjust so that I don't overthink about stupid things. He's always willing to talk to me and he always reassures me. He's too good for me and he really tries his best to comfort me, so I want to make it easier for him and try to get better.

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TLDR: I've always had jealousy issues and currently I'm jealous of my partner and our new friend and it's bothering me. I'm getting jealous over little things such as high fives and fist bumps. I'm afraid he'll enjoy their company more than mine. I've accidentally hurt my partner during a time when I got jealous because of him and our friend talking while they were being too close to eachother it made me uncomfy. My partner and I communicate about this and I want to get better and stop feeling like this for the both of us.

I, myself, know that how I feel and what I do is wrong, but I don't know how to change myself or how to cope with this feeling so that I don't do anything hurtful to anyone. I want to get better for my partner and I, I want our relationship to work. If anyone knows any coping mechanisms or self improvement tips for this kind of stuff please tell me what to do.