It may not be possible to determine the exact cause of your symptoms without complete clinical evaluation and merely on the basis of a picture. These bumps can be due to any allergy, inflammation or infection. From the image and the details you have provided in your post, this sounds like rosacea. Rosacea is a cutaneous disorder primarily of convexities of the central part of the FACE, such as FOREHEAD; CHEEK; NOSE; and CHIN. It is characterized by FLUSHING; ERYTHEMA; EDEMA; RHINOPHYMA; papules; and ocular symptoms. Treatment goals are to control the condition and improve appearance. Avoid any possible triggers for the flare ups. Rosacea may be influenced by smoke, weather and certain food. So avoid any of these as much as possible. You have been taking oral antibiotics which appeared to have improved your condition. Oral medications for rosacea may help to improve the condition. It is best to see a dermatologist and get evaluated. Treatment will depend on the underlying cause. Hope it helps.
Good luck and take care!