Usually, your thyroid stimulating hormone (TSH) will be too low if your thyroid is hyperactive. The pituitary gland, which emits TSH, is signaled that there is plenty of thyroid hormone circulating and therefore, the pituitary does not need to stimulate the thyroid any more with TSH.
Sometimes, there is something like a tumor on the pituitary causing depressed numbers of hormones that would otherwise be normal.
If your too low TSH is because your thyroid is too active with its hormones, symptoms can be extreme nervousness, anxiety, inability to gain weight and weight loss. You can feel weak, tired, have a rapid heart rate, difficulty breathing and feel down. You can have hair falling out, shaky hands, increased sweating & have red skin that's warm and possibly itchy as well. If you have Grave's disease, you can have protruding eyeballs that are red, a thyroid goiter, unhealthy finger and toenails, etc..
I myself have low lab results, symptoms include weightgain, fatigue, low libido, no energy, neck pain etc, please post your lab results including ranges so we can try and help further? Hope this helps x