Even if you did turn up with an injury in May, the Medics would never let you onto the Y List (remedial unit) if the knee caused you problems. You would have brought an injury into RMAS, and it is not the responsibility of the Army to fix people who broke themselves in civvy street.
Ask the OCAC if there are any extenuating circumstances whereby you can join the Sept intake. I doubt it, because it is almost certainly full by now. The Admin staff may not look upon a 29-year old with a knee injury with great relish.
Perhaps you SHOULD HAVE TOLD A GROWN UP! Did you think of telling anyone at Sandhurst? Did you contact them when you injused yourself? Did you not do any prep and bottled when you realised what you were going into? If you want it bad enough, TALK TO THEM!
Not that much of a lifetime of ambition if there is a fallback plan, job, PhD really.
You will not have much luck anyway if you wanted to join an infantry regiment at the age of 29, with a lower-leg injury. If you pulled your thumb out of your arrse, and in a spate of proactivity phoned Sandhurst's Admin Officer (Capt Benbow), you may be able to talk your way back in.
Try to sound enthusiastic, rather than dripping on about injury/family problems/your age/your array of contingency plans.
Chin up! Capt Benbow always recommends the RN or the RAF to everyone who gets injured iredeemably at RMAS. If you can't run 1.5 miles in just trainers and shorts, you are never going to be able to do battle PT, stretcher races and Ex Long reach.