You should discus this with your doctor. Your pharmacist may be a good resource as well. Tramadol is an opiod. Those can cause shortness of breath in some people. You may be more prone to that with your COPD. I have severe asthma though and I take opiods at least weekly for back pain. I have no problem with it. It just depends on how your body reacts to it. If you are concerned, you could ask your doctor for safety measures you can take should you become short of breath.
I hope that helps.
Take care and feel better.