Is it normal for the doctor to squeeze and pinch your face after injecting juvederm?

It's hard to speak for another injector's technique. It may be that he was molding the filler for a better result. I recommend following up with the Dr. about your concerns and feedback. Best, Dr. Emer

I am sorry to hear about your experience. This indicates an inexperienced injector. It usually means the filler was not placed where the injector wanted and they are trying to move it. This leads to more bruising and shorter longevity of the product. I recommend seeing an expert for future injections. 

Different techniques are used by different injectors.  Many use very little to no massage with injections.  I would suggest speaking with your doctor about your concerns.  You may want to select a different injector for further treatments.

This is usually seen in the more inexperienced injectors. It indicates that the filler wasn't placed exactly where the injector want to place it and they are trying to get it to move. This leads to more bruising and shorter longevity of the product. 

Facial fillers are injected to improve the volume and contours of the face.After injecting, facial fillers can be molded for a better result. By massaging the product with firm pressure, lumps can be smoothed out and hollows can be filled in. If this causes discomfort, your doctor can give you intermittent breaks. Throughout any injection, I ask my patients if they need to take a break in between pokes, because I can get a safer, better result if my patient is relaxed instead of tense and squirming. Safety comes first.