Have only one blood shot eye on and off for a month, dr says allergy or virus and gave drops, but I feel like I should be more concerned?

See eye specialist. It would be unusual to have only one eye affected if it's allergies, and unusual for the same eye to have a routine viral infection over and over. There are a number of possible causes, and an ophthalmologist would be the best person to sort it out. I hope it clears up soon!
Maybe. If there is no change in vision or pain, not an emergency, but a virus would have been better by now, and allergy is possible, but may want to see an eye specialist if not improving.
Several possible. Several possible causes. A recurrent red eye is commonly due to dryness, a vascular disorder (hypertension), allergy or too much Aspirin or Aspirin products (ecotrin, alleve etc.). Your blood pressure should be monitored and controlled if elevated. You should avoid visine (gets the red out version) and use artificial tears instead (visine also makes a brand of this). See an eyemd if persistent.