Feeling dizzy when working out. Low energy and ambition. Had TSH elevated, fT3/4 normal. Should I start taking l-thyroxine or test for addison's first?

Neither. If your TSH is only borderline elevated (5-10 range) and free T4 is normal you are very unlikely to feel better after starting l-thyroxine as fatigue is due to low free T4. Addison's disease is very rare and in addition to fatigue the symptoms which suggest it are weight loss, abdominal pain, salt craving and darkening of the skin. Your symptoms could be due to lots of non-medical issues.