Hope that you are doing okay with your shoulder. I can't really offer you any advice as I'm not really sure how you know that you tore your rotator cuff, or if you did. Were diagnostic tests done (other than the physical tests which your physio did)?
Yesterday I just had a (probably very) small tear repaired under arthroscopy. I also had a small spur removed, which is likely what caused the tear. So mine wasn't due to any accident, and judging from symptoms, was probably existent or getting sawed away at by the spur for years. As we age, particularly if there are things maybe slightly out-of-whack (and most of us are slightly out-of-what, to a certain extent, I believe), and/or we abuse our shoulders a lot with sports/lifting/whatever . . . we can have problems. My shoulder surgeon said that something like 90+% of us have some type of rotator cuff tear in our lifetimes. Most of them heal by themselves and in a year are all better, or maybe sooner, or some maybe need surgical repair. I guess it depends on how bad it is, and how/if it heals.
Anyway, a few years ago I had MRIs on both shoulders, and both of them showed small tears in several places. At the time, I was 53 years old, and years of sports probably didn't help. I had one shoulder "cleaned out" at that time, and had to wait for this one until now due to other injuries and getting time off work. But I did okay with the unrepaired shoulder, with pain coming and going, and a few cortisone injections (but you don't want too many). I have had to avoid swimming any stroke where my hands come out of the water (and I have designed a creative way of still swimming freestyle with an underwater arm recovery stroke!). And sometimes it would really bother me, such as when I had to use crutches for two weeks, and or I would fall on it skiing or whatever, and sometimes just using a computer mouse too much (yeah.). And I probably have had at least four or more courses of physical therapy over the last 20 years for my shoulder issues, working on stabilization and such. But I think that I am just one of those people doomed to have bad shoulders (and other joints), and, um, I'm getting old.
Actually, when my former surgeon (since I have changed insurance, had to change surgeons) cleaned out my first shoulder two years ago, he didn't even sew up the tears - he cleaned out the joint so that the bursitis would allow the cuff to sit back down where it needed to to heal itself, as the bursitis had been holding the cuff up too high and the tear could not heal (called a lift-off lesion). It has been pretty good since then, though he had warned me that the bursitis might recur, and lately it has been a little annoying at times.
So good for you, that you are working on therapy, and I hope that it helps. I am not sure that a tear can really be diagnosed without an MRI or going into the joint with a scope. But maybe the therapy will help you get back in shape without surgery (last resort, though arthoscopy isn't too bad if it is just a tiny tear like mine). It might just need to heal. IF that's what it is. I don't know much about the Canadian healthcare system - is a physio a sports doctor? For some reason, I thought that they were physical therapists. Anyway, most of the shoulder exercises which have been prescribed for me over the years have involved a lot of internal and external rotation exercises, and one doctor told me that rule of thumb is to never do any exercise where you cannot visualize your hands either directly or in your peripheral vision. So no behind-the-back pull-downs, stuff like that. And he also told me "no push-ups, ever". You'll get all kinds of advice from different practitioners. See what works, and allow things to heal. And if your doctor doesn't seem sure and/or you're not getting better, maybe get some diagnostic tests done (xrays, which don't always show much in the way of tears, or better yet, MRI) so that you know what you are dealing with, or get a second or third opinion.
I've been taking glucosamine/chondroitin for years (so does my cat with a repaired ACL, ha ha!), and I don't know if it helps at all. It is more for general joint issues, not a torn cuff. So not sure that it will help you specifically for your problem. I suspect that the physio told you to ice it a lot to allow the inflammation to go down? It would seem to me that you would not want to be lifting the shoulder up too much - not letting your elbow leave your side much - until the tear heals.
Best of luck to you!