I'm sorry that this is a rather late response to the original query ...... but it may, at least, be helpful to others ...
1) If you are worried by low TSH assays, the following recent research may offer you some reassurance:http://www.endocrine-abstracts.org/ea/0021/ea0021OC5.6.htm
2) If your doctor is similarly worried, likewise!
3) The OP (original post) implies that she is taking other than straight T4 (Levothyroxine) ... if you are taking thyroid hormone relacement containing T3 (for instance, natural desiccated thyroid e.g. Armour Thyroid), it is very unwise to take a dose not long before your blood test - T3 is much faster-acting than T4, and if you do .... you are quite likely to see unrealistically high T3 and low TSH results ..... leading to quite unnecessary alarm and despondency if your poor doctor thinks you are taking just T4! ;-)
4) To the OP, I find it very worrying that you might feel any need to fool your doctor - if, for whatever reason, you feel unable to confide fully, you need to get another doctor ASAP. You do have that choice, and if you fail to use it you may do yourself (and your doctor) grave disservice.