Some suggestions:

1 . Ruminating is bad yes. Recognize it as hurting your social life. For each day that you allowed yourself to ruminate, in your room, write a 200x on a sheet that you will not ruminate because it's hurting you socially. Let it sink into yourself that you have to stop it immediately next time you get to class. Keep doing until you stop this habit. Look for what you should be doing instead. Write a 200x on a sheet that you will listen to the lecture and get the most of it.
2. Make it a goal to get to know your classmates names and introduce yourself. If achieve those, write them down.
3. Ask the person next to you, for their opinion about the lecture, as you were talking to your sister/brother/cousin. Then after they answer, introduce yourself.
4. If you're uncomfortable introducing yourself, you can practice it in your room every day for an hour until you sound confident. It's often a fake it until you make it.
5. Catch yourself when you think negatively. For example, when you see others sounding comfortable talking to each other. Tell yourself, so what? That's normal. And just because they appear confident, it doesn't mean they are internally. They might be anxious but it doesn't show. Or they might just had a lot of practice because they join clubs or have a job involving people, they are around people a lot, etc. But you can you get a lot of these practices too if you put yourself in social activities and make an effort. Social confidence doesn't happen overnight if they are shy and self conscious. It takes a lot of practice and faking confidence until you make it.
6. Get a part time job if you can where you are forced to interact with the public. You will see when you are forced to interact with people, every single day, eventually you will appear confident. If getting a pt job isn't feasible, join social clubs and events. Take acting lessons.
7. Social interactions can be overwhelming when you are not use to it. Accept any social mistakes and forgive yourself. If you felt slighted or insulted or you said something wrong, or felt so uncomfortable and didn't respond quickly or appropriately, etc., it's normal. You must have self love and determination that you are worth the trouble and hard work. Think of the bigger picture about is this really relevant to keep dwelling on? Will it help you in any way to rehash it? Talk to a counselor.