If you have symptoms but no fever and are a asthmatic do they test you for the coronavirus/covid?

Depends: A lot would depend on the availability of testing supplies & covid in your area. The group at most risk are those short of breath with minimal exertion. This group would more likely need hospital care. Most others would be better off self quarantining & avoiding a testing site where they may be exposed. Controlled asthma has not been found as a big risk factor.