With new prescription glasses, my left eye sees clearly if right is covered, but right eye is blurry if left is covered. sign of wrong rx?

Possibly: It is definitely possible the rx is incorrect. However, if the glasses are not lined up appropriately, it may seem like your prescription is off. I would take the glasses back where you had them made to ensure proper alignment and if that seems ok, recheck the prescription.

Maybe: Sometimes the back base curve of the lens can't be tolerated even if the rx is correct. I use the analogy of shoes. One manufacturer is comfortable while another is not even though they are the same size. Make sure you take your older lasses with you so they can be tested by a geneva lens watch. Also some times a larger or smaller lens size can be problematic causing distortion.