My opinion is "Why not at least try it?" My guess is that it would also be great physical therapy of just the sort you need. But if you want a more experienced, clinical, and professional opinion on that, try posing your question on a sports medicine forum or going to a sports medicine doctor for a quick evaluation and consultation. I'm also puzzled about exactly what your concern is if the trauma happened over a decade ago. And what the issue of taking many breaths is.
Are you saying that you're stuck with a chronic condition of lowered lung capacity? In that case, my guess would be that that's not irreversible (and again that playing a wind instrument would be likely to improve it). Based on my own experience (never had a collapsed lung, but came close once when I broke a collarbone and five ribs in an incautious moment on a motorcycle track), you may have never had the correct PT program at the time (or not stuck with it), and are still involved in a kind of "guarding" behavior with your breathing. But a decent sports med (or maybe ortho) doc and PT tech could probably tell you the story on that pretty quickly.
I'm 71 and definitely notice a lung capacity problem compared to twenty years ago, but "almost 30" strikes me as way too young to give up on playing tuba unless you have a genuine and competently diagnosed chronic condition that couldn't be improved. And even if you do, so what? You can still play the tuba. Just get a smaller one (like an F or an Eb, or even a small bore BBb) and go for it.
Gary Merrill
Wessex EEb Bass tuba (DW 3XL or 2XL)
Mack Brass Compensating Euph (DE N106, Euph J, J9 euph)
Amati Oval Euph (DE 104, Euph J, J6 euph)
1924 Buescher 3-valve Eb tuba (with std US receiver), Kelly 25
Schiller American Heritage 7B clone bass trombone (DE LB K/K10/112/14 Lexan, Brass Ark MV50R)
1947 Olds "Standard" trombone (Olds #3)