Not really honestly. Low-profile AND comfortable costs money, pick one. That is a very tight budget, even inexpensive office chairs from IKEA are around $200.
You could try something like this, it's well reviewed and small. I would bet your butt would not appreciate being on it for hours though.
I like this one. Bought it for myself a year ago. Friend needed a new chair and she liked mine, so I bought her the grey one for this Christmas.
simple is often best, here's two highly rated amazon office chairs: http://www.amazon.com/Boss-Fabric-Deluxe-Posture-Chair/dp/B0019QGVIE/ref=sr_1_1?s=furniture&ie=UTF8&qid=1432245978&sr=1-1
Hours at my desk, and I bend the back to the level of comfort I want.