Anemia is the most common cause of fatigue , dizziness
sensation and shortness of breath
Get your Hb levels repeated.As there is pressure of baby on diaphragm so there can be shortness of breath which is normal.Hypertension
can also cause these symptoms.As you are 37 weeks pregnant so you have to bear with them for one or two weeks as they will subside after delivery.
Best wishes and good luck