Am 33 now, but was told I had blocked tubes after an HSG when I was 30 (actually on my 30th birthday - great present, eh?). I had been TTC for over a year when I had the HSG done.
My RE told me that surgery to re-open the tubes does not increase your chance of falling pregnant naturally by much. IVF produces much higher success rates. I did an IVF cycle and got pregnant the first time with my gorgeous DS.
The good news is that you are young. If you have to have blocked tubes, so much better to find out at your age. I remember how devastated I was when I got the news, but now its a distant memory.
I truly wish you all the best.