The only way to quickly tell if you might be infertile is to see if your fallopian tubes are blocked with mucus. They can do that sometimes with an ultrasound or laparoscopically.
The way most people find out if they are in fact unable to get pregnant though is ttc-ing and not getting pregnant. Most doctors won't go through fertility testing until you've been ttcing for a year, or sometimes for 6 months.
Even if they do find heavy mucus or blockages, it doesn't mean its impossible to get pregnant. Meaning, you shouldn't rely on that as birth control.
If getting pregnant is your aim, and there are blockages, there are minimally invasive procedures you can do to remove blockages. And of course sometimes IUI is needed to help move things along.