I think you might be a bit overcautious

or at least I hope you are! I have OCD, and I think provided that you were never hospitalised for it and you otherwise have good references it should be OK. I had to go to an occupational "specialist" doctor several times when I was applying for jobs. Most of them clearly didn't know the ins and outs of OCD.
In fairness, I would never tell them I had a drink problem, but your occupational health doctor has no right to look at your long term medical history (I'm almost certain they have no right to request it). Thats for your GP only! (If it isn't, given my history, I may aswell throw in the towel

)