$100 is a very strict budget, especially nowadays. You would have to be hunting for used parts on services like FB Marketplace, Offerup, Craigslist, etc. I started with an old workstation a few years ago (i5 3470, 4gb ram, 250gb hdd) and upgraded that for a while ( 4->20gb ram, gt 1030->1050->1060 (had to buy a seperate psu for this one), 1tb ssd+4tb hdd, etc). Having people you know also interested in PCs can also be important, since you can be first in line when they upgrade (that's how I got a 1070ti for $50 !!).

But I would really recommend getting a job when you can; money will come in like you've never seen before. If you get a $15/hour job (assuming you're in the USA, but really applicable anywhere) and work your weekends, that's $200 a week. You'll be good to get lots of upgrades or a whole new machine in not too much time. Even at $10/hr you won't be suffering for long.