DNA analysis of both parents and both parents is needed. Alpha carriers often cannot be detected except by DNA analysis. One of the parents carries alpha, and most likely an alpha mutation and not a deletion, as the deletions moderate the effects of beta thal, rather than causing a worse condition. However, there are alpha mutations, such as the triplicated alpha gene that contains 3 genes instead of 2, causing an excess of alpha globin to be produced. Combined with a deficiency of beta globin production, this can cause an intermedia condition that may require occasional transfusions. One of the parents carries some form of alpha, so both should be tested.
You carry at least beta minor, which can leave one fatigued. I would suggest that you also have your vitamin D level checked, as deficiency affects more than half the people on earth and deficiency will also add to the tiredness and fatigue caused by beta minor.