Good morning, Lauren.
Jealousy is a rather aggressive emotion and can be expressed in dreams violently, so that part is no surprise. When you strike your friend, you are allowing your anger to surface.
There are a couple of possible meanings for the removal of your shoes. One is that you don't want to be in the position you currently find yourself in, meaning, if you were to let your jealousy show, then you wouldn't want to be "in your shoes." Another possible meaning is a desire to get more in touch with your basic emotions. Both could be true at the same time; dreams can be very economical of their symbols that way.
The classroom is a learning situation, and science in particular is a subject oriented in logic and reason. In this setting, you are sitting beside the very same friend that you punched, putting the two of you on equal footing.
When I put this all together, what I see is this: your jealousy is making you behave irrationally. If you can get more in touch with yourself, both emotionally and logically, you will find that you and your friend are on equal footing so far as this guy is concerned, and your friend is someone that you will want at your side in the future.