Have a look here about what your employer's responsibilities are with regard to your health and safety. Risk assessment is obviously one of the main ones, and if they are refusing to do a risk assessment for you, particularly given your problems in the past, that's not good enough and you should draw their attention to their responsibilities.
It's not unreasonable of them to want to know what your doctor says about your condition. If you are not off sick presumably your doctor thinks you are fit for work at the moment?
You say they are 'focusing on your work-related injury' as if that is a negative thing. Have you had confirmation from a doctor that it is work-related? If so, them focusing on it is not a bad thing, surely?
Similarly them paying for an occupational health appointment is a good thing. OH specialists will encounter lots of similar conditions and will be able to advise both you and your employers how to handle the situation.
You mention wanting to sign the accident book but I'm not sure the accident book is for things like developing pains in arms/shoulders. I'm not a health and safety expert but I would use the accident book for things like trips, falls, burns, cuts, one-off incidents, not ongoing, developing conditions.
You mention that you can't afford a solicitor. Why do you think you need one? Are they threatening to sack you or something? Or is this to try to force them to comply with their risk assessment responsibilities? You could ring the HSE if they continue to refuse to risk assess you.
I think the visit to the OH specialist is a good next step.