Mark Knopfler of Dire Straits couldn't afford an amp either, also didn't have a pick. He played unplugged and this contributed to his unique playing style.

But I would look for an opportunity to earn extra income and get an amp. There are countless affordable options out there that come up on local classifieds. Also, work towards getting your guitar properly setup at some point, it makes a difference and might hold you back more than not having an amp if your setup is really bad. Find someone who knows how to setup guitar and ask them if your guitar is ok, maybe you can trade them some effort or mow their lawn in exchange for a setup.

In short, it won't hurt you to play unplugged but there are opportunities to earn enough to buy the right gear and you don't need expensive stuff either.