I’ve continuously have been using the plunger on both our main and master bedroom toilets. Initially, it startyed only in the master bedroom toilet. As soon as you put a little TP in the bowl it plugs up. After vigourous plunging it is clear? Do I need to use a snake/auger or have to clean a trap in the sewer line?
First I would try a toilet auger on both toilets, because it is the low cost solution. You can get a toilet auger at Home Depot or other big box stores.
However, since it is more than one toilet, you’ll probably end up snaking the main line after the two toilets come together. You can either D-I-Y or call a drain cleaning service.