Damaged mine years ago when I played rugby and really should have had an operation. Did the injections for a while and they help, but can cause problems later in life through calcification. My doctor recommended physio instead and I had six sessions which really helped especially with the stuff you can do at home. No weights just a giant elastic band and resistance exercises. I have some pain killers for the odd day or when I have slept funny. I would certainly get your doctor to refer you for physio.
As a judo coach/player for over 40 years now, I have had operations on both shoulders with the same issue you have. Most the time cortisone injections do help but only for a few weeks of pain relief as its only the inflammation that it is treating. As someone has mentioned a good Physio is a better option. They will prescribe a range of exercises to help build the supporting muscles to make the area stronger and improve your range of movement. However if your rotator cuff muscle is torn it will need repairing. It could also be an impingement issue, I.e. Calcification build up on your bones that are hitting the underneath of your shoulder blade, or tearing in to your muscle. Either way you ideally need an mri scan, that's the only way really to know for sure what the problem is, your money would be better spent getting an mri as you could throw a lot of money at Physio, injections etc that may be pointless. My shoulders are good again now as the surgery for these problems is fairly routine and although painful post surgery, they only take around 6 weeks before you get back to normality. I noticed the pain originally when I found it painful washing my hair, I.e. Lifting my arms above shoulder height.
Had my operation about 6 months ago and its been pretty damn good,still get the odd twinge but no pain at all. Its key hole surgery and your home as soon as you can pass water after the operation which was about 4 hours.Get it done asap and enjoy life again.
I had the MRI scan and to quote the guy at the hospital it was a mess inside. I was advised to live with it rather than have an operation(s). Touch wood since the physio and the fact I do the exercises I have had no problems.
Try getting directly in touch with the physiotherapy departments, particularly if you have more than one hospital that is accessible to you - consider also that some health authorities use external partners to deliver the service within the NHS.
MANY of them now do self-referrals, i.e. YOU simply call them to make an appointment, with no need for a doctors referral ... ALL of the major hospitals local to me do this, and I speak from very recent experience, with both me and my partner having initial assessments last week, within 7 days of us first approaching them. [:T]
 The other half fell over the doorstep in march last year and moaned like hell about the pain and restricted movement in her arm/shoulder, but refused to go to the doctors and get it seen to for 6 months, when she eventually went, the doctor diagnosed a tear on the rotary cuff and referred her to the hospital,there was a 4 month waiting list,when she first went she said no way was she having injections because of what other people had told her, she has been having physio for a few weeks, and had to go and see the consultant again last week and he injected it while she was there, she said 2 days after the injection it felt a lot better and she had got more movement back, but the arm and shoulder was very weak from lack of use, she has to go back and see the consultant again in a few weeks and he told her if it is not a lot better she may have to have keyhole surgery in the meanwhile to carry on with physio and the exercises, so it is now wait and see.[:T]