Could Hair Fall And Dizzy Spells Be The Symptoms Of Hypothyroidism?

my hairdresser today said that it looks like my hair is falling out and asked if I had anaemia or a thyroid issue. I do have beta thalassemia but in my recent bloodwork the results were low heamoglobin but normal iron levels. I m also a vegetarian but do eat a good diet. Could I be experiencing hypothyroidism? I also experience dizziness when standing up, need to take naps during the day and have had regular periods but irregular flows (one month light, the next heavy).