If you have your heart set on physio, then I wouldn't go getting yourself into three years of debt studying something that you aren't really interested in. I qualified as a physio 3 years ago, and there are vast differences in how the different health professions work in practice.
SLT - dietary and fluid assessments, swallowing alongside obviously the speech and language stuff.
OT - Discharge planning pretty much unless you specialise into something like hand therapy or stroke, but you are unlikely to do that until you are senior. The juniors I work with are largely doing home visits, measuring up for equipment, sorting out social services etc. It's a world away from what you would do as a physio and I would urge you to think about this before jumping down the OT route.
Sports science - I just wouldn't. Take nothing away from the hard work etc of doing this degree, but everyone I know who has done this ends up as a personal trainer in a gym, or doing something completely different like a graduate management scheme in the city or something. I'm sure one or two do find their way into elite sports, but I would say this is the exception not the rule. Do a 3 month personal trainer course and some extra courses ontop of that and save yourself three years if you want to coach people. If you are certain you want to get into high end coaching then might be worth thinking about, but reading what you have put, doesn't sound like you want to be training Usain Bolt.
Sports Therapy - Again, nobody I know of has made a go of this. There is no route into the NHS in reality. Yes, you have any willing provider now which means that sports therapists etc could work in the NHS, but the reality is that it is physios who are employed. Where I work, we have two sports therapy graduates employed as band 3 rehab assistants, so two levels below what a qualified physio goes in at.
Osteopathy - Great, but it's a 5 year slog, no NHS bursary or funding, and again, you will be going private solo from the off. Not a bad thing necessarily, but you are unlikely to find employment in the regular sense from this.
Radiographers - go around zapping people and taking x-rays with big bits of equipment. There is probably more to their job, but I never see them for long enough to enquire what.
Dieticians - To do with diet obviously, and you would have the option to diversify into sports or elderly or whatever. If that sort of thing floats your boat then great, but again, very very far removed from physio.
If employment options are what you are after, then physio is a good shout. At the age of 20 you have time on your side, even if it feels like you don't. I was 31 when I started my physio degree and came out at 34. I was far from the oldest on the course. I would strongly advise against doing a course simply because you can't get into physio or medicine or whatever. It is three years of your life and a not too insignificant financial obligation. Of course, if you have parents or a trust fund or something to pay for it all then who cares, but if you are going to be coming out the other end with 30 grand of debt and a degree you don't want, it is worth thinking about.
It sounds to me like you have all the right things on your application - work experience, a knowledge of the profession, so it must have been something at interview that you didn't do. Who knows why the others rejected you without interview. I have sat on interview panels for the uni I studied at, and I know that the feedback we give can be a little sparse.
Hope all that helps. I'm very keen on helping the next generation into the profession, and this site gave me a fair bit back when I was studying/applying, so post back any further concerns.