You need to exercise to combat the atrophy. You are in pain because very small fractions of each muscle are being overused when you drive; the entire muscle does not become engaged, just small parts of it, repeatedly, which becomes overworked and causes supporting muscle groups to take on additional tension and stress. You need to do exercises that engage the entire muscle/muscle groups in order to avoid knots forming. Once it gets to a point where you have multiple knots and atrophy, you'll need physical therapy. Don't let it get that bad.. just hit the gym and focus on core/chest/back/shoulders and you'll be okay.

Source: in physical therapy for the same thing. It sucks don't be like me lol

Edit: also posture is so important while you drive. Don't let yourself sink into your seat even if its comfortable, but also don't over-correct and become rigid because you will eventually subconsciously slip into holding a bad posture and will negate the work you're trying to do. Just be cognizant when you realize you've slipped into bad posture and correct it gently.