Yes,it is still possible to be hypothyroid in spite of having normal TSH
There is a condition called as HASHIMOTO'S THYROIDITIS
which is auto immune in nature.The diagnosis is made on the basis of clinical picture along with finding the presence of anti bodies called as anti thyroid peroxidase
and anti thyroglobulin
Even if one or both of these is positive, treatment will not normally be initiated for low thyroid function
unless there is the presence of a raised TSH levels and possibly a low T4 level too.
However it has been seen that if you give low dose THYROXINE to such patients ( having clinical picture of hypothyroidism
but with normal TSH and T4 ),there is dramatic relief in the symptoms.
Other possible causes for your symptoms could be....
Low VIT D levels
You must discuss with your doctor about all these possibilities and get the required investigations done.