“After bypass surgery, should I go for a pulmonary check up too?”

most certainly a lung doctor can help address some of your concerns

Do you have any pulmonary symptoms? Short of breath? Wheezing? What did your cardiologist recommend? With some insurances, you need a referral to see a specialist, so your primary doctor or the doctor doing the surgery and your follow-up usually has to recommend pulmonary care with a referral through your insurance for your insurance to pay for a pulmonary check up.

In general, even if you do not have or had lung problems prior or after your surgery, seeing a lung specialist is a good idea. Bypass surgery can cause several lung complications such as paralysis of the left diaphragm, pleural effusion (fluid around the lung), among others. If you have a history of prior lung diseases like COPD, asthma, or have persistent shortness of breath, cough, or chest pain in areas other than the sternum surgical incision, for example, then you very likely need to see your pulmonologist.
I hope you are doing well after your surgery and my answer helpful.

Alex Lechin