Did your doctor do any other thyroid tests with TSH? If so, please post those and include reference ranges, which vary lab to lab and have to come from your own lab report.
Once on thyroid meds, TSH is often suppressed and is no longer a useful diagnostic. How do you feel? Do you feel hyper? Typically, levothyroxine is adjusted in 12.5-25 mcg increments. Halving your dose is a sure way to put you on an overmedicated/undermedicated rollercoaster.
No, your doctor is trying to get your level under control, so to do this sometimes they have to adjust your dose. In your case (and in mine), the level was cut in half, so your level should re-adjust. You should not change medications unless your doctor wants you to.
My question to you is are you taking brand name medication like Levoxyl or generic? If you are taking generic, studies have shown that unless you get the SAME generic company, your labs can go all over the place because the generic companies can vary slighly. My Endo. MD insists on brand name only because of this. About a year ago there was a problem where the brand name was not available and I had to go on the generic, and sure enough my blood levels were all over the place. So this might be something to look into.