Yup, you don't *have* to compete all three. You should check with your gym though- my DDs gym requires kids to compete all 3 until they reach at least L10 (maybe elite). The lower levels of tumbling are pretty basic though. L3 is cartwheels and round offs an d L4 is robhs (2x, separately).
In our T&T competitions you do not need to compete all events. Our comps have 4 events
1. Individual trampoline
2. Double Mini
3. Tumbling
4 Synchronized trampoline
Some people compete, 1 or 2 only. Also most kids are in different levels for each different apparatus.