You do need a snake, but you also need a plumber. It's probably the main building drain, which should be augered from the main cleanout using a heavy-duty power auger. In an older home the most common cause for main-drain blockages is tree roots. In the unlikely event that doesn't fix it the plumber may need to pull a toilet and auger from there.
A hand-held snake is very unlikely to do any good. They are useful for clearing small blockages in fixture drains and toilet traps and so on but they won't do anything for a major clog in a main drain. Once you see the 3/4" power auger you'll see what I mean! Also, don't use a chemical drain cleaner--it won't help this problem and it's not good for either the plumbing or the plumber.