As you have congenital hypothyroidism I don't understand why they don't prescribe Natural Dessicated Thyroid Hormones which contain all of the hormones a natural healthy thyroid would, i.e. T4, T3, T2, T1 and calcitonin. Would mother nature provide these if not required?
The very least your doctor could do is add some T3 to your T4.
Always get copies of your blood tests and get a print-out from the surgery of your latest one with the ranges as labs differ. You don't take levo on the morning of your blood test but take it after as it can skew the results and have it as early as possible. TSH varies throughout the day anyway (I doubt GPs know this).
As you are having symptoms, and if you took your last blood test later in the morning or after taking meds, ask for a new Thyroid blood test, plus Vitamin B12, Vitamin B, iron, ferritin and folate get a copy and post on a new question. Don't adjust medication yet.