Pain in my front shoulder muscle - suggestions? (Hybrid cycle) I ride a hybrid cycle to/from work each day (10 km / 6 US miles each way).

The handle bars are flat, and I ride with my thumbs gripped around the handle and 2 fingers close to or over the brakes (I feel safer).

Last year I rode every weekday without problems, but this year I am getting some pain in my front shoulder muscle on my right side.

I was doing 20 chinups and 50 pushups each day, so I cut these out for a while to see if it would help. I'm still cycling and still getting the pain. It hurts most when I sleep at night (I am a side sleeper) and when I wake up I feel the pain in a small area (front deltoid).

I am wondering if other people had similar pain and any suggestions?

Perhaps riding with my seat higher, or riding a racing bike would help, or even those little "verticle handles" that can be attached on very the end of my handle bars pointing upwards.

Maybe my muscle development was assymetric with all the exercises that hit the front (cycling, pushups) without balancing exercises for the back?

I'm 39, 6 foot / 86 kg and in otherwise very good physical shape.

Thanks for any tips / advice

PS. I'm a computer programmer by trade and use my right arm often during the day with the mouse.
DISCLAIMER: This is by no means a definitive answer, but one of the options you may want to look into. Also as this borders on a medical advice, this is only meant to give a kind of guidance, not a prescription. 

So one way to deal with pains caused by a substantial amount of cycling is to get your bike fitted, i.e. measured to see if your seat post is high/low enough for you, your cranks are of correct length and so on. 

In your case you may be leaning too much (or indeed not enough!), which could strain your back and/or shoulders, so it could be the case you need your stem shortened (or otherwise lengthened!). 

I had my stem shortened from 100mm to 90mm due to me leaning too much and getting quite a lot of pain in my shoulder blades. However I've had my bike professionally fitted.