Can working out on stationary bike irritate rib muscles 3 month after pneumonia? and cause tension in neck?

Conceivable: If your irritated rib muscles are on the same side you had pneumonia would suggest a followup X-ray making sure you did not develop a pleural effusion on that side, otherwise common self limited complication of pneumonia. For the neck tension a variety of other possibilities are to be considered, but if there is a significant increase in your bike exercise slowing down will give you the answer.