First, I sympathize with you feeling dizzy, the feelings of guilt, etc. Don't be too harsh on yourself; that just causes mental anguish with no benefit. This is a tradition that everyone around you follows and you were under tremendous social pressure to do so; the suffering you've caused to those animals is horrible and irreversible but it is also commonplace in the world we live in right now, and probably way less than that caused by an average westerner over the course of the year.

I don’t think I will repeat it next year, but what am I even meant to do?

Not repeating it sounds like a good first step. This tradition is violent and unethical, and it's best to learn from your experience and not make this mistake again. Choosing vegan options is also a good step individually. You might also want to join local vegan groups, if there are any, to organize with others against animal exploitation. Speaking with like-minded people may also help you process the feelings that you have, and help prevent more animal suffering in the future.

More generally though, and I'm sorry to say this, the teachings of Abrahamic religions are not compatible with equality or real liberty, not for humans, definitely not for animals. You will (eventually) have to choose what is more important to you: god or humanity.