I have an OSL limitation on my medical, meaning I can only fly with another qualified pilot.
Yeah... It's a thing. It was imposed upon me for a few months 18 mounts after I had recovered from an accident (The medical people were pretty slow in notifying me). They were entirely off base, and when I finally proved they had no grounds, my CAT 1 was restored. The problem was that in the mean time, my airplane does not have dual controls. So, instead of flying my airplane solo from my home runway, I would drive two hours through Toronto traffic to fly with a friend in his plane. I guess the imagined risk to the public of my non existent medical condition if flying, did not extend to the risk to other road users while I drove. I remain unconvinced of the whole wisdom of the regulator's medical team.
Following my accident, I did not fly for seven months while I recovered. When I was ready, as required by the wording of the regulation, I went for a flight with an instructor. I had never met him before, and he had no preconceived idea of how I flew. It was apparently well, as that 172 fit like a glove. I felt like I'd flown it three hours the day before. Getting signed off was not a problem - with the instructor anyway, the regulator, 18 months, and 150 hours of flying later was not so easy!
So CS, go and build experience, keep yourself fresh while your full medical is restored.