The fact that you're doing no exercise on it may not be helping matters...if it's been like this for 5 months it may be less likely to need rest and more likely to need stretches (which i know you say you're doing) and strengthening by walking around on it. i know you've said it's painful, but surely the gps can give you stronger pain killers if gentle exercise is what's going to heal it.
the nhs process or referral etc takes a long time for everybody. be firm and say you want a scan and a better solution than just stretches, but take it upon yourself to try to make it better too ie by gentle exercise and walking on it a bit.
don't go to A&E, it's not an accident, or an emergency, they won't be able to offer a longterm solution because thats not what they do, and it won't get you noticed by them, you'll just be added to the 'prescribed painkillers' pile. go back to the GP.