I've had the full feeling in the past, although it hasn't been bad lately.
I understand your concern about the meds. If it's contraindicated for people with breathing problems then I think you have to wait until that resolves.
I often get partial and sometimes full relief from doing this:
-- heat my neck (typically with the carex bed buddy back/neck wrap)
-- neck stretches, primarily for the front of the neck
-- first rib adjustment with strap -- hey you don't have one so you can skip this step!
Takes me at least 20 mins and sometimes 40.
Good luck!