I am 36/female and having increased fatigue, weight gain, brain fog, increased depression and exhaustion. my gp order labs; my tsh is reported as 3.54 and my free t4 is 0.8, both say on my lab references these are within normal range, but are they?

Different labs often use different units & I have to conclude that you don't have an underactive thyroid according to your lab. Have you been checked for anemia or iron deficiency? Chronic stress, sleep deprivation& depression are common causes of chronic fatigue. Discuss with your physician.

They are for most labs in normal range. Work up is normally extended to other common conditions that can cause symptoms like yours, your current doc remains your best reference at this point. Physical exercise always helps in such circumstances, has to be gradual as injuries are possible when starting.