Hi folks,
to the OP: Please stop bench pressing at the moment if you can. If you can't, try completing unilateral dumbbell pressing with the good arm only for now.
Additionally, there is one thing that can not be emphasized Enough: Posture, posture, posture. Without examining in person your form with exercises it is difficult to tell if there is anything that could have precipitated this injury. My experience and studies suggest that the neck position in various exercises has the capacity to influence cervical spine health, especially during bench press exercise.
The ideal would be to have a full assessment of the musculature. As one response has already stated, find out exactly which muscles and ultimately which nerve roots are affected. I would want to know specifically is it at certain levels, and or specific roots?
The one other thing that may be missed out is the Serratus Anterior strength test. If the lateral pectoral Nerve is affected, this significant scapular stabilizing muscle may have had significant atrophy. I would want to get a full scapular examination as well. Bench movements imo are completely out of the question considering altered bio mechanics and neuro-signalling to the surrounding musculature.
best of luck