Unrecognized, starter and schooling events usually don't require you to have a USEA membership.
You'll want protective boots that do not retain water... woof boots, splint boots, etc, they should also have a strike pad on the back of the tendon for the front legs.
As long as your helmet is ASTM (or whatever the initials are) approved, you should be ok. You will also need a crash vest and arm band.
You're currently jumping 2'9"? Hmm... Novice goes up to 2'11" so you may want to start out at beginner novice, just to keep it easy and safe. Currently I event BN but we're schooling 3'3", keeps the xc and sj questions easy.
Splints are common in all breeds. I don't think I've ever owned a horse that didn't pop a splint due to regular work. Lower level eventing is probably ok for your guy, but since the unsoundess is from an injury, you may want to have it checked on a regular basis to ensure the work isn't causing problems.
Good luck! Welcome to eventing... it's a lot of fun and everyone is pretty cool.
If your horse says no, you either asked the wrong question or asked the question wrong
And God took a handful of southerly wind, blew His breath over it and created the horse