You should never feel pain. The "no pain, no gain" saying does not apply in your circumstance. Do you have any known injuries?
There is a good possibilty you are not lifting correctly. I would suggest lowering the current weight you use to perfect your form on all chest excerises, and then increase the weight gradually. Spend a little time researching proper movements.
If you still feel pain, try using circuit machines in stead of free weights for a while. They tend to cause less stress on stabilizer muscles in your arms, and in many instances isolate your chest muscles well.
Geoff