Hi Marie, glad to hear you do have some union support.
It depends a lot on how your OH works, your manager will write a referral which they should discuss with you first, to check that you consent to a referral and the reasons why. The manager can ask for specific questions to be answered by OH, for example an estimated date of return to work.
You may see a Nurse or a Doctor, sometimes a Nurse may telephone you first to assess and make a convenient appointment time for you to go in and see someone of that is needed. Mention to them anyway what you have said about the foot rest, as that doesn't sound right to me based on what you have said, especially if it is upsetting you.
Your discussion with OH and any medical details including your diagnosis are strictly confidential, and you should be asked to fill in a form with different levels of consent first - you can ask to see the report before it is sent to your manager and then request any changes if you want to, although they will not change facts they may re-phrase stuff if you are not happy with it, before it is sent back to the manager.
The counselling is also confidential, and I very much doubt it would prevent you from getting another job, they are not allowed to ask about your health any more before offering you employment, and it sounds like you will get the job to resolve your current situation, so if it helps you, I would try not to worry too much. It is a positive move to seek help when you need it and you should have completed your six weeks by the time you started any new job, so they couldn't say you were not fit on that basis anyway as you could always put a positive spin on it if asked.
Good Luck with your application and I hope it all works out for you x