I'm in 37th week of pregnancy, my vagina started to ache. Is it normal and a sign of pre-term labor?

Not usually. Vaginal aching is typically an indication of pressure from pregnancy, not usually preterm labor. Labor pain is cyclical.... It comes in waves and lasts for about 60 seconds or so. The vaginal pain you describe is more typically a stabbing, aching pain that is constant. Sometimes a warm bath at this stage in pregnancy can feel good.