Will there be a potential problem using a DOUBLE vapor barrier as in the following setup?

Bedrooms were cold/drafty. Removed the drywall on the outer walls, sealed all leaks and put in new insulation. The insulation has the paper vapor barrier attached, installed toward the heated room. As extra protection, I put 6 mil. Plastic sheeting over the framing, then drywalled ( attached with screws and not yet taped).

I know in certain high moisture situations vapor barriers/double barriers should not be used-just wondering if it is OK with this extra protection that I added. Thanks

Yes you should be OK, there is no way moisture will go through 6mil, but tape all the joints, outlets etc to avoid anything getting by the plastic.
Remember that the moisture will be inside the rooms, think about some way to let it, before it finds its own way out.

Good luck Roger