I want Botox, a filler and CoolSculpting under my chin.

There is no medical contraindication to the treatments listed and your sinus condition.  However, depending on your recovery, you may have subjective symptoms.  Botox and fillers should be no problem.  Any type of submental treatment may add a sense of tightness under the chin.  It does not cause any objective impairment; however, subjective tightness under the chin along with your nasal obstruction and choking at night may add to a subjective feeling of discomfort when lying down.  It all depends whether or not you would be able to put up with these temporary subjective sensations.

No, these procedures won't negatively impact your sinuses. I recommend following up with an ENT.  However, for the chin, VASER liposuction in combination with ThermiRF are best for contouring the chin in those who are candidates, but Kybella can be used as an alternative and needs to be combined with thermage/ultherapy/exilis or coolsculpting for good results. I recommend getting a formal evaluation with a facial sculpting expert. Best, Dr. Emer

If you have not already, I would recommend that you see an ENT doctor to evaluate your sinuses and the mucus problem that you have.  There may be a remedy for these issues.  Botox, fillers and CoolSculpting under the chin should not have an impact on the sinuses or mucus production.