I only had a second degree tear too, it was a funny shape though and they cocked up the stitches. It wasn't life threatening but it was uncomfortable having sex and even using tampons and it was also affecting me psychologically.
My GP was very sympathetic- I deliberately booked in to see a woman who had children- and referred me right away. Even though I went private in the end (didn't like the NHS consultant), it would have only taken me a few months to get fixed on the NHS.
The GP told me that there's a clinic at the hospital that deals solely with post-childbirth fanjo repairs because it's such a common issue. Don't feel like you're being fussy, demanding a designer vagina or any of that stuff- this happens a lot and it can be fixed! Can you see a different GP? The one you saw doesn't sound very sympathetic- was it a bloke?
Recovery was waaaaaaay easier than childbirth. I was only in pain for a couple of days, walking around normally after about a week and was back running 2 miles within 3 weeks. It depends on the surgery you have done but I found mine much easier than recovering from childbirth because you don't also have to look after a newborn, have massive, swollen boobs etc. I managed with a few days off and then back to looking after a 4 yo and almost 2 yo.
Good luck with getting a referral, I hope you manage to get it sorted out :)