1. My own son, age 19, has had chronic asthma since he was 2, and with appropriate use of medications and learning to "take responsibility" for his illness he has managed very well mentally and physically, not using the asthma as an excuse for anything, yet realizing he does have some limitations. If your son has had severe asthma attacks and/or knows that if he doesn't take his medicines "perfectly" he will be in big trouble, that malingering fear can produce a chronic anxious " backdrop" that unconsciously taints all his "performances". I'd like to be secure in my parental knowledge of how he "really is" psychologically with having asthma. Kids at this age often are exposed to the mortality issues of this disease through newspaper articles and/or TV health reports. He may be more worried than you know.
2. I would like to explore the notion that your husband's recent remarriage now completes his having his parents completely broken up "forever". Kids often hold out hope that their parents will get back together as long as one has not remarried. This recent marriage may have closed the book on all that hope and/or revivified all the fear of losing you both. Many kids believe that if they were better kids, i.e. performed perfectly, their parents never would have become angry with each other and divorced.
3. You may want to step back and see if you have subtly sent him messages throughout his childhood of what you consider to be acceptable and expected of him in his pursuits. Perhaps encouragement in areas that interest him where the "success factor" is not present would be a worthy goal, i.e. just playing and having fun, alone, with you, or with other kids where the only "goal" is having a good time.
4. If his life is lived in constant fear of "failing" at everything, he does need more support now than you alone can give him, but he should be "allowed" to be a kid who just plain sets high expectations for himself and while it may trouble you to see him demand so much of himself, you may just have to lighten his load as much as you can. Realize that this may be one of his personality traits that has positive sides as well, that it will be tempered as he ages.
I'm sure a trusted, talented therapist who has worked with kids who have your son's family background and self-demanding personality will be of great help. Let me caution you, however that just because this current therapist is a trusted friend that does not mean he is the best choice for your son. Ideally, your son should do the choosing after meeting with a few top choices you have found; the person should be a good "fit" for your son's personality.
Good luck and thank you for being such caring parents.