Q-tips count, and they are DEFINITELY non-flushable!!! They can easily get jammed in the plumbing and collect debris and cause exactly what you're seeing. Yuk!
I have a friend who installed a basement bathroom in his house. Since it was below the water eject line he had to install a shit pump in a hole he jackhammered in the basement floor. These pumps are meant to be untouched for decades... Well, somebody flushed something "sanitary" down and the string got caught up in the impeller blade, not an enjoyable operation fixing that...
Take a wire hanger, cut one end and carefully stick it into the hole were the water forces out of just in front of the hole that goes down-out. Also look under the rim,lots of small water holes, the wire will help unclog calcium & hardwater deposits and should help restore forceful water flow to help return the flush. I am just guessing that maybe the thing is not clogged in the drain. To help confirm this, Take a bucket of water and dump it into the toilet all at once, if it flushes, you have water flow problems and not drain clog.
Be non-conformist and buy an old-style high volume flush toilet in Canada, thats what I did when I bought a house with a first generation one piece no-flow toilet
http://totousa.com/toto/totohome.asp I would check the site for a distributor near you-I was lucky and found a few near me here in MA-its no B.S. they are the best by far-even recommended on "This Old House" show. I paid decent money for mine- but well worth it- I had some trouble last year- new toilet -new house-even though it was new it was a cheaper one the builder put in-and I had some water problems (leaks-flushing- you name it) now I am a believer-my friend just built a new house and he put Totos in his house-its like one of the first things he shows the guys when they go over- like AL Bundy and his Furgerson Tim
I am not a plumber. If you don't want to call a plumber, you are going to have to do it yourself. Remove the toilet and get it over with. If you do not know how, find out. It is very simple to do and is not messy at all. Common sense applies. You do not want to force anything stuck in a toilet to move further into the drain system. The reason you are removing the toilet is to get to the offending blockage from the bottom. You will probably have to replace the wax ring or rings, depending on the bowl model. If there is nothing in the toilet itself, try pouring a few gallons of water directly into the open drain to see if it backs up. Sewer gases will come up thru the open drain but can be stuffed temporarily with a towel or bucket.
Now be a real adventurer and get your hands dirty!
I had a dream last nite - the problem was not an obstruction, but a problem with the flushing system.
There are some lo-flow (1.6 gal) marginal flushing systems out there that do not work well. Did you pour a couple of gallons of water into the bowl itself, and did it drain fine? Lo flow toilets need propulsion to get the waste thru the system - be sure that the flushing system mechanism is operating properly prior to removing the toilet.
Your other toilet is probably the same brand, so at least you can watch what happens in flush mode.
The thread title should be: "My toilet is clogged. I have tissues". Nothing constructive to add here except, that I feel your pain, man. My sister in law clogged one of our toilets a few years ago. Had to call a plumber. He told me he found "what in the business we call a white mouse". Yup one of them wimmins' sanitary products. Ever see the episode of Married With Children where Al builds his own bathroom? He installs a toilet so powerful "it will suck your arm down". May the flush be with you.
Careful if you buy this as these specifically states not to be used on toliets. The brand I had was called "sewage king" and these things can kick butt (I used them for my Dad's rental house). I remember on one of the ones I unclogged you could feel the ground vibrate about 50' from the house as it was pushing the obstructions, most likely "white mice" based on the number of women in the house at the time.
Umm, some people actually do. My older sister used to be a store manager for Hechingers (not around anymore, death by HomeDepot ) and she used to tell me that some people have actually taken a dump in the display models in the store... Of course, it's not hooked up to plumbing or anything.