Kathi
I am sorry you are going through such a rough time.

a doctors diagnosis will do nothing for your son. But a kind and wise therapist or counselor can do a great deal.
Existential depression is very real and can be devastating. In the accompaniment of heritable and or biochemically based depression as in the bipolar family of mood disorders it can be very serious indeed. If your son had cancer would you not get him treated?
Labeling your son will not help him you are right, but having a safe outlet to explore his feeling about the meaning of life, Gods expectations for him, and why sometimes life seems unbearably hard. you and your husband may not be the right "safe outlet" for him right now. Even the Christian community might not seem safe to him to be his honest self and express his feelings that might not be so pretty. Many PK and MKs have difficulties with needing to measure up to the expectations of the Christian communties that they live in. Being gifted with a dad with bipolar only amplifies it all the more.
That parable of the Talents is a heavy weight to many. I have always wondered what happened to the guy who tried to use his talents and lost them. and i have always been a little bit angry with God for not putting a fourth man in that story.

Being angry at God is not always tolerated in Christian communities. Your son may have feelings that he feels aren't Christian to have and aren't allowed. He may think he has to be perfect to be an adult and its just to hard to get there with all his imperfections. You never know.

Secular psychological professions are often hostile to faith systems. But there are many types of therapists out there that may help your son. In my opinion the important things are that they respect his faith, understand existential depression and have wisdom.

One group of professionals that might fit are Pastoral Counselors. They are trained in a faith tradition and also in psychological counseling. They can be very helpful.

I am making alot of assumptions here and i appologize if i am off base. But please consider if your son might be clinincally depressed and seek guidance.......
I will pray for you.

to the board -- I also appologize for getting more specifically religious that seems to be the norm accepted here. Faith communities can really hurt the gifted but they can be sources of great strength. There is existential depression but there is also existential joy.....