I do think that anything can be over done/over used. This would include gemstones too. Apparently something in that bracelet gives you too much of a good thing. Turquoise is a great crystal, and known as a sacred stone to the American Indians. I do wonder if Hemera is on to something and perhaps you need to cleanse this stone? Over all it is known as a great positive stone, and is spiritually, emotionally and physically and mentally positive.
I think again, as Hemera mentions, you should probably make sure it is the stone itself that is draining your energy. When you have made sure it is the bracelet, perhaps try wearing it only once in awhile. You may also want to cleanse it--and you can google to see how to safely do this to your bracelet. so many stones cannot get wet, or shouldn't be in the direct sunlight for hours on end, etc. so be sure to research the safest way to program and cleanse your turquoise bracelet.
I have a moldavite gem that I wear on a chain as a necklace. It is too strong for me, and so I now only wear it when I'm going to divine for someone. It is way too powerful for me, bringing on massive migraines and such. So now, we've found a happy medium. I wear it only when divining and then when I am done, I take it off and put it away.
*did a bit of googling on turquoise and found it is recommended to clean your turquoise once a month in a bowl with tumbled hematite stones and then recharge it by setting it with rock crystals. It is also advised to keep it out of the light of the sun.