working on the computer, riding the bike... sounds like postural weakness to me.

Core muscles do effect this pain, because they give your upper body its base of support.

So, I'd say do some core exercises and do some prone flyes/rows/rowing machine. Make an effort not to slouch at the computer (treat computer time as a posture exercise) and not to sag on the bike (another posture exercise opportunity).

You might also want to raise your bars a cm or two, just during the interim, until you are stronger.