Providing that any mh problems are not going to prevent you from being able to do the job, or that the job isnt going to make the problems worse then there is no reason for them stop you working. Self harm shouldnt stop you as long as its hidden and not in danger of infection/won't be worsen by the stress of work.
I have had multiple dealings with occ health as a hca and as a student and so long as Ive been functioning ok Ive been allowed to work. Actually I've found them more supportive than anything. There have been times when Ive been prevented from working but its when Ive been a complete and utter wreck and realistically not capable of it (ie I couldnt compose myself for long enough to make it to/from work or through a shift).
I would be honest......if you're not (and they can ask for information from your GP) you can lose your job for dishonesty. They are not there to try and stop you, they are there primarily to support and enable people to work effectively and to the best of their ability, saying your unfit is a last resort.
Go show them what you can do