Lab work has a lot of value to it but needs to be interpreted carefully, just because the results are "in range" doesn't mean you will feel well, they need to be in the right part of the reference ranges.
There is lots of information on interpreting Lab numbers here
There are some excellent resources on lab work, including many that you can order without needing a Dr, on the STTM Lab page
RT3 and FT3 tests can be ordered without a Dr and there are sources of this in the Yahoo RT3 group files area. In particular Econolabs and Life Extension are currently the cheapest sources for RT3 testing.(updated 10/10)
A cautionary note is that a FT4 reading that is over 1.4 is a marker for RT3 being high.