If you toilet and shower go to a common drain, then you may need the services of a plumber, sorry to say.
But to start with, open up the trap of your shower drain and remove any hair clogs from it, next clean it out with 1/c baking soda followed by 1 cup white vinegar, when the fizzing is done, rinse well with hor water, a good amount of it. This may just do the trick for your shower drain, leaving the toilet drain to be solved.
From here, I would use a plunger, as you probably have already done and had no results that have worked. You could rent a snake or buy and try that, it is kind of a shot in the dark when you really don't know what is blocking the system. If no luck with the snake, call in the pro's to see what the actual problem is, they have cameras that will literally look into your drainage system and diagnose what is wrong and how to fix it. Best to you.
If there are trees along the drain line from the house to the sewer line, you may have tree roots that have penetrated the line. Only a plumber can clear the line. $50-$100 depending on distance.
If it becomes an going problem, you can flush a cup of rock salt down last thing at night. That will let the salt sit in the line long enough to kill the roots.
Hey Kathy: Give this a try. This looks long and complicated, but it's not. Well, it is long, but not complicated:)
If stopped up, get a really long zip tie, cut slits going down the side, one on the right, one on the left, all the way along to the bottom, and twist it. Then, tie a string on the top really securely, and tie that around your finger. This will keep it from falling down the drain:) Then, stick it into the drain and jiggle it around and lift it out to see if anything stuck to it. If so, do it a few more times to get as much gunk out as you can.
Then, You will need this: (this will work on the drain and toilet. Same directions starting here)
A small box of baking soda
1/2 cup vinegar
At least 1 quart of pretty warm water. Not boiling hot or you can crack the porcelain on the toilet.)
If both are stopping up it sounds like you need to call in a pro to remove tree roots (RotoRooter???) This doesn't sound like a DIY project to me.