I had a torn Cartilage last year, if thats what you have, then the recovery period should only be around two weeks, and you'll be able to carry on playing Both Squash and badminton.
I play Table Tennis to a reasonable level, and have no problems, My Nephew, who had the same thing, is back playing Rugby.
The thing to do now, is get it checked out, if your gp, sends you to a Consultant, don't settle for an X-ray, you need an MRI scan to see the full extent of the damage.
Real problem is the waiting list on the NHS, so if you can go private, go for it.
I wish you all the best with it, now get round to your gp.