How would a person know whether it was an allergy or asthma causing breathing problems?

Doctor Eval. Asthma is recurrent bronchospasm and airway inflammation and it can be caused by allergies. Allergic symptoms can include bronchospasm. So, in order to know if bronchospasm is due to allergy, you would need to see your doctor for an evaluation.
Asthma. Allergies can trigger asthma, which causes breathing problems, so it is all related. Asthma occurs when the tissues of the airways become inflammed, constricted and secrete mucus. This causes the typical breathing problems, wheezing, shortness of breath, and cough. Trigger for asthma include allergies, infections, exercise, cold dry air and stress or anxiety.
Asthma. Asthma has several triggers, one of which is allergies. Therefore, when allergies cause "asthma-like" symptoms, it is asthma, period. It people where allergies are a common trigger of asthma symptoms, controlling the allergies can often help control the asthma. This includes avoidance, medications, and allergy shots.

Related Questions

Posture related breathing problems. I'm unable to exhale fully and don't know if its asthma, airway remodeling, allergies, or something else.?

No. That is a common and overrated opinion about bad posturing. The only known posture related breathing restriction is related to rotoscoliosis or abnormal bending and rotation of the back bone -- most 'bad' posture is not caused by rotoscoliosis but more from lack of fitness and obesity.

I have weird itching sensations in my lungs (not on my skin) and a bad dry cough, but no sinus or breathing problems. Never had allergies or asthma.

You need to be. Examined/have your chest listened to. It sounds like you could be wheezing. Even without a history of asthma or allergies, it is possible to have them now. It also could be a sign of bronchitis or pneumonia, so please call your doctor and get checked.

Should I live with a deviated septum or get the surgery done? I'm having breathing problems from asthma/allergies and have bad post nasal drip.

Could be allergy. I would first see a board-certified allergist to determine if your symptoms are due to allergy & to what. The surgery would not help asthma nor underlying allergies.
Have it repaired. Nasal airway function and draininge are inter-related, and can have many headaches, infections, worsening of asthma, etc if left alone. This is a true functional problem and should be recongnized as a medically necessary procedure. I suggest you contact a qualified sinus surgeon for care, and have appropriate xrays to insure sinus outlet obstruction is not also a factor.