Nouna,
Most adults will not shows any hemoglobin Barts, even when they do carry alpha thal, so electrophoresis is not always useful when alpha is present. If you are a thal carrier, and it is likely, you carry alpha thal. You have low Hb, low MCV and MCH, which all indicate thalassemia. Your iron levels are normal. The electrophoresis shows no HbF and low HbA2, so beta thal is ruled out, leaving alpha thal as the only real possibility. Putting that together with a family history of favism, makes alpha thal very likely. A DNA analysis can confirm this, but is probably not necessary.
Because of your symptoms, I recommend that you take 5 mg L-methyfolate daily. This is most important for alpha thalassemia. I also suggest B Complex, natural vitamin E and magnesium be taken daily. Also, get your vitamin D level tested and report back with the number. Vitamin D deficiency is very common and deficiency causes all sorts of issues, like fatigue, tiredness and a low immune system. It is extremely important that your level is in normal range.
You need to observe and look for any substance that may cause favism. If you notice sudden tiredness with no explanation, review what you have been exposed to. Avoid all broad beans and also avoid chemical fumes and scents as much possible. Avoid cigarette smoke as well.