Do the fuel pump causes pressure to build up in my gas tank?

My 1999 Suzuki wouldn't start. I discovered gas was not getting to injectors. When I sprayed starting fluid in intake inlet, it will start & run until starting fluid runs dry. I changed fuel filter (old filter had rust color slug in it). I can't tell if fuel pump is running, because I can't hear it nor see it running. What confuses me is the pressure that is keep building up in system. Could my lines be block. What is another way to test to see if I have a good fuel pump. Note: I checked relay & switched it.