Here’s a breakdown of your sentences and which ones work for your situation: 1. I'm tied up to Aaaa team. 
❌ Incorrect * "Tied up to" is not idiomatic English. 2. I'm tied up with Aaaa team.
 ✅ Potentially Correct, but awkward in context * "Tied up with" usually means you're busy or committed to something, but it doesn't convey the idea of being a fan out of obligation. 3. I'm stuck to Aaaa team.
 ❌ Incorrect * "Stuck to" isn't natural for this context. It sounds more like you're physically attached to the team. 4. I'm stuck with Aaaa team.
 ✅ Correct * This works well! It conveys that you feel obligated to support Aaaa team, even though you'd rather be a fan of Bbbb team.