T3 & T4 Values are normal But TSH Low in thyroid test.

The TSH value is what is indicating hyperthyroidism.  When the numbers are low, this indicates hyperthyroidism and when high indicates hypothyoridism.  I know it sounds like the opposite of what you would expect but that is how it is measured. For the other two tests, each lab has their own range for normal and this varies from lab to lab.  You need to know the cause of the hyperthyroidism to best treat it.  It can be caused by autoimmune diseases such as Graves disease or Hashimoto's thyoriditis or by nodules or goiters.  To rule out the autoimmune diseases, blood tests need to be done to measure antibodies and often they do a thyroid uptake scan to diagnose Graves disease especially.  While you were given two options by the doctor, there are actually three options, the third one being thyroid hormone blocking drugs like Methimazole or Carbimazole.  In my case, I have Graves disease and I was insistent with my doctors that I would not undertake the two options that you were given to choose from.  So I did a lot of searching to educate myself and learned about supplements that help in addition to prescribed meds.  The ones I took based on a research study I read were L-Carnitine 3,000 to 4,000 mg per day, vitamin D3 gelcaps 1,000 mg daily and Magnesium, 200 mg daily in addition to Methimazole.   I think your Mom can benefit from taking the same supplements.  

I am in the same boat...T4 & T3 are now within normal range but TSH is 0.03 (normal is 0.400). I have Graves and taking all the necessary supplements including L'Carnitine 3,000 mg. I am scheduled for a thyroidectomy end of June. I also have Graves ophthalmopathy which is the only reason I am getting the surgery.