I think my A/C compressor is seizing up?

[Black88GTA]

As the title says...I think my A/C compressor is going out. The problem - whenever I activate my heat (using the "auto" button) the engine seems like it bogs down a bit, the car accelerates noticeably slower (and not very smoothly), the transmission bangs gears at low speeds and seems to shift at odd times, and the car in general is unresponsive and sluggish. It behaves sort of like it's dragging the brakes. And, I've been getting horrible gas mileage. I don't know the exact number (only been thru one tank since I got it, and forgot to reset the trip when I filled it), but I think it's in the range of 10 - 11 mpg I have had the heat on almost the whole time though.

My car does have brake issues (which will be taken care of probably this spring), but this is a different problem, because the car behaves normally when the heat is turned off. I tried activating the heat and looking under the hood, but I didn't notice anything out of the ordinary. Everything seems like it's working properly when inspected.

I know some cars activate the A/C compressor when the HVAC is used (even when heat is on) to pull moisture from the cabin air. Does the SVX do this? I have a feeling that it might, and that it is my compressor causing these problems.

Does this sound like it could be possible, or am I way off base? Does anyone else know what it might be / have suggestions on how to fix it?