Hi A.,
I am actually a result of my mothers fallopian tubes being blocked.
After I was born my parents attempted to have another child. After years of trying, they sought help. Eventually they found my mothers tubes were blocked. One was completely, the other something like 80%. The doctor told her the fact she had one child was quite something. But obviously, it can happen. Her tubes were blocked by scar tissue. She apparently had a childhood illness of some sort that caused the scar tissue. They cleared it out and she became pregnant within 2 months.
Don't worry yet until you know what the blockage actually is. In addition, hopefully the blockage could be cleared.
Good luck!