B737 First Officer reports lining up with Runway 21 at Biggs during a low visibility visual approach to Runway 22 at ELP. A go around is initiated when both ATC and the crew detect the error.

Narrative

We were using LNAV direct AGUAS anticipating the visual into Runway 22 at El Paso. We were at 6;500 ft MSL and getting very close to AGUAS when cleared for the visual to Runway 22 at El Paso. Visibility was poor due to blowing dust and I had not picked up the runway yet. The runway was at the 10 to 11 o'clock and I was in the right seat as pilot flying. The Captain called out the runway and I located a runway at 11 o'clock. Appearing to be high; I immediately continued to configure for landing and remained visual. Noting that my LOC and glide slope were not matching up with my visual picture; I notified the Captain. The Tower was preoccupied on the radio at the time and was unable to assist us as we were lining up on the wrong runway. At some point slightly below 1;000 FT AGL; the Captain noted that we were lined up on Runway 21 at Biggs. At the same time; El Paso Tower notified us of the same. I initiated a go-around and returned for a safe landing on Runway 22 at El Paso. I should have briefed the potential hazard of similarly aligned runways at EL Paso and Biggs. I should have continued to use my NAV equipment in the process of navigating to the correct runway.