Yes acupuncture can, and regularly does, help with addiction, withdrawal from prescriptions drugs and, very likely, the swollen tongue, etc. More importantly, however, acupuncture does extremely well with the root issue - treating the anxiety. I would strongly suggest you consult with an acupuncturist in your area and give them about 3 months to get your son in good shape.
Now all that said - and I am by no means an advocate for modern western pharmaceutical medicine - but, the side effects you are describing from cymbalta are certainly not common and the doctor was well within his ethical boundaries to not describe those. Even the addictive part is somewhat over stated (not denying it is an issue though) - you can come off of cymbalta fairly easily when done properly. Cymbalta is no more or less addictive than any drug in it’s class. I mention this only because, generally speaking, doctors are doctors and your son’s swollen tongue is more likely an allergic reaction to something else rather than something a year in from cymbalta, so that should probably get checked out and waiting for another physician many not be worthwhile.
Now with that said, this process of coming off medicines is all that much easier when done with acupuncture, possibly with the addition of properly prescribed Chinese herbal medicine. We do it all day long with this and much stronger medicines that have far greater addictive aspects and have never once had an issue.
But, yes, coming off on your own with no other treatment in place can be difficult and is not advised without direct consultations with the prescribing physician.
The thing is, from many physicians perspectives, you are not coming off the drugs - ever, in most cases, so they don’t think to describe that aspect because they are medicines of “management” -not- “treatment” which is the exact opposite of Chinese Medicine. Both have their place in many cases and in some western medicine excels, in this range of issues, however, their clinical success in resolving those issues is poor.
For the most part with regards to anxiety the only two things that have shown strong clinical success in resolving these issues is acupuncture and cognitive behavioral therapy.