Your heart, lungs, gastrointestinal functions, etc., may all feel fine and indeed BE fine, now and for quite a while. My comment about nerve innervation has more to do with what to keep an eye out for, and what
may be affected years down the road (so when or if it occurs, you'll have had some insight).
Pilates (pronounced: Puh-LAH-teez) is a type of exercise, like yoga, tai chi, etc. It's probably closest to yoga, but without all the body contortions. The primary focus has to do with postural alignment and how to recognize what is wrong, and how to fix it.
There are many books and tapes on the subject without necessarily having to work with an instructor or video.
Many postural digressions occur over time, and what you experience now is the beginning of what becomes much worse over the course of time. It will only get worse if you do not actively try to correct it.
I have a similar situation as you do, which is a kyphotic dorsal spine and flat lumbar spine with loss of lordosis. For me, it's related to a spinal injury, and unlike you, I'm limited to what things "I" can do to fix it....you have more opportunities.
The backstroke is highly recommended (in clinical exercise therapy as well as in Pilates) for correction of this.
Use care in abstract thinking about "pulling your shoulders back" because this may make it worse. It is not about pulling them back. To identify the structural aspects, you need to think of the source, which is the scapula, not your shoulders.
Depress them, and retract them (the scapula),...take your focus away from movement of your shoulders, and take it deeper from the origin close to the spine. Your scapula should lie flat. In kyphosis, the tendancy is to wing. A slight winging now can be serious protraction later on down the line.
An example (as it pertains directly to
lifting weights) is this: If your form is poor on the bench press, for example, and you do not keep your
shoulder blades back, flat, against the bench, and if you reach up and out, lock out your arms, reach towards the ceiling and releasing the tension on your pecs, this very action, this lift, results in scapular protraction, and will be just one of what I'm sure are many ways, in which you contribute to making this worse.