Ditto on everything Bosmom said.
Personally I wouldn't take synthroid because I have heard and known too many that have not done well on it. If your Mom is doing well on it, then it may work fine for her. I have a neighbor taking it for many years and she is doing o.k., her hair actually got thicker, most people complain of hairloss with Synthroid.
Natural meds are Armour, Westhroid and Nature Throid, they all have both T3 and T4 as well as all the other T's your thyroid would make if it worked properly. For many the natural works much better than the synthetic.
There is also synthetic T3/T4 called Thyrolar and synthetic T3 called Cytomel.
Any person with any heart problems has to be very careful with adding T3 to their meds.
I take Nature Throid with added Unithroid (syntheticT4) to keep my T4 level up because the natural meds have a lot of T3.
Hope this helps you.
Take care