Bathroom plumbing issues

I own a house that was built in the late 1940's in northern Louisiana. I started having problems with the toilet not flushing well a few weeks ago, and it has since gotten progressively worse. I believe there is a clog in the line that provides drainage for all the plumbing in the bathroom, because now when the toilet is flushed, it will drain into the tub. It used to be that this would only happen when the toilet was flushed frequently, or after someone took a shower or a bath, and then it would slowly drain out of the tub after it had backed up. Now, it won't even drain at all. I am also having similar drainage issues with the sinks, although the toilet thankfully doesn't back up into them. I don't really know much at all about plumbing, but I can't really afford a plumber right now. I'm assuming that this is beyond a little bit of drano? Any tips? Do I REALLY need a plumber? Thanks!

I assume you have a septic.
Start by checking the septic tank.

We don't have a septic tank

You may have a simple clog or you have roots or a broken pipe. The most common cause in a house this age is roots. You need to call a plumber or sewer cleaning service.

drain.

Usually people with this problem call me when it happens. They want an immediate solution, so they don't check on the Internet first to see if they should call a plumber.

Maybe you could continue to wait until the clog is so bad it backs up into the sinks. Sorry for the sarcasim, but pal, you need a professional to auger you drainline and evaluate the problem. It isn't going to go away by itself, and you are right, chemicals won't do it. You'd better move this up on you list of priorities in the budget and find a way to pay for it.