I am taking good care of myself with a 1000 calorie diet and daily exercise, but I am losing hair anyways. Can I have a thyroid problem?

Both hypo and hyperthyroidism can cause hair loss and precipitate genetic balding if you have the genes for balding. You need to see a doctor and get your thyroid checked out.  Also, your extreme diet can cause balding to appear especially if you have the genes for balding.