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I will save you the cost of a "phone" call. To resolve this issue has only a couple options. Since plunging didn't work the only home remedy left is to purchase a toilet auger (about $15- 20) at a home improvement or hardware store. This "snake" will rod out any clog remaining in the trapway of the toilet if in fact that is the issue. IF this does not work then it is time to hire a professional drain cleaning company to remove the toilet and rod out the sewer drain pipe. It is entirely possible there has been a slow (partial clog) all along that the baby wipe has finally completely jammed up and fully clogged the drain.
If you aren't getting any water replaced in the bowl after a flush then you need to check and be certain the flush valve and flapper in the tank is working properly. Flapper should raise when the handle is flushed and water should drop from tank into bowl and the flush valve should allow water to refill the tank. That would be a separate issue from thr clogged drain. The closet auger is only long enough, and designed to clear out (remove or push through) any obstructions caught in the toilet internal trapway (gooseneck) itself. It is not long enough to remove any obstructions such as tree roots or other blockage that may be occurring further down in the piping system that can cause toilets to clog up. I will be unavailable for the remainder of the day as I have to work today 11-5. Sorry, was hoping to remedy this in completion last night.