Sometimes if it doesn't unclog by using the plunger, I pour bleach into the toilet and let it sit for a while = usually a half hour to an hour and then flush it and usually the bleach softens whatever is clogging it up.
Bleach is a cleaner. Won't unclog toilet. If a plunger won't work.
Try this product.. https://amzn.to/2MzNSVT
It might help, I have not used it but heard from a friend that it is very helpful..
I've had great luck with dumping half a bottle of dawn soap in. Let it set half hr or more and flush.
It REALLY has worked !
1] Take a bucket of hot water from the tub and pour it down the toilet as fast as you can without overflowing. The extra force of the water and the temperature should flush out any clog.
2] If you think there might be a problem when you flush, pour in some cheap dishwashing soap and let it sit. Then flush [empty the tank], the soap should soften &/or lubricate for the flush to go down.
I have used both and use #2 often.