Hi im a smoker and I have asthma. .. I have my breathing going fast after I go up stairs. My question is can it be due to smoking? Or my astmha

Both... Asthma can be exacerbated by exercise in some patients. Smoking can lead to increased airway inflammation which can also trigger bronchospasm in some patients. So, both your asthma and smoking could be contributing to your symptoms. You need to quit smoking asap in order to decrease your airway inflammation. Your symptoms and even your asthma are likely to improve. Your doc can help with this!
Maybe. Smoking can cause pulmonary disease and contribute to heart disease. If you have increasing shortness of breath going up stairs which would be considered exertional, you should go to your doctor and have it checked out to be sure if it is asthma, or your heart. At any rate your asthma needs to be controlled and you need to be certain you do not have anything serious in your lungs or heart.