I'm assuming this breakout is on the side you sleep on. Wash your pillow case every second day, and use tea tree oil to spot treat pimples. Yea tree oil is a natural antiseptic and astringent.
It might not be an allergic reaction, but bacteria from sweat/drool at night. Put a fresh towel on your pillow every night that way bacteria doesn't have a chance to grow on the pillowcase itself.
--aesthetician.