I had a very similar experience, and paid for a second opinion. Despite the private doc's report that there was nothing wrong with me, the RAF medic's word was final - no flying for you, young snapper (strangely, some years later, the same RAF doc cleared me for fast-jet back seat flying
). I suspect you'll be in much the same boat - sorry to be the bearer of bad news. I was given the thumbs-up for a PPL, much like yourself.