My recent blood test determined my tsh was 5.35 and my ft4 was 13.3. is my doctor right to consider this normal? i feel awful.

Borderline low: I assume the ft4 is in "pmol/l". That level is normal. The TSH level is mildly high and suggests that your thyroid level may be slightly low overall. The vast majority of people with these readings will have no symptoms related to their thyroid. However, there are some people who are sensitive to even mildly low levels. You should have it repeated along with thyroid antibody (tpo, tg) levels.

No: The elevated TSH level indicates hypothyroidism. If you felt fine it would be considered subclinical but since you feel 'awful' that means you are definitely hypothyroid and require thyroid hormone supplement to help you feel better. The underlying cause is usually hashimoto's thyroiditis. In young female adult individuals we see this when somebody had a delivery or miscarriage or began a bcp.