No. From my point of view, not at all. From my point of view you are actually at a very priviliged position. A few other comments that you curiously did not reply better explain why there is no exploitation here.

That said,I am not one of those people that think that privileged people should not complain. At all. Every has the right to try to improve their life. In your case, I believe you should practice negotiation. Try negotiate your salary. If dont get a raise and dont get a better offer elsewhere, maybe you are earning a fair salary. Try negotiate the deadline. Explain why is asking too much to do all that in 4 months. Maybe you will learn that their expectations of quality are much lower than yours. A logo and a website can be made on one morning if there no expectations at all.

Or maybe you will end up your negotiation with a raise and more time.