I think i have anemia because i don't eat red meat. do all non-meat-eaters need blood check for anemia?

Not necessarily: Anemia can be caused by so many factors. You probably are referring to the anemia that are caused by deficiency of nutrients i.e. Iron or vit b12. In addition to red meat, there are a lot of other foods that are rich on vit B12 and iron - for instance- other kind of meat , poulty, egg, milk- have some amount of vit b12. Spinach, beets, beans have are rich in iron. See your doctor for evaluation.

Anemia and meat: No. Most people get sufficient iron from other sources. Young women can become anemic from heavy menstruation, but young men generally do not become anemic whether they eat red meat or do not.