We have used a plunger, snake, bleach, expensive draino and nothing seems to be working. The shower drains but into the tub. Then when we plunger the tub the water goes back to the shower and vice-versa. Does this mean I need to hire a plumber? Or is their something else I could do to fix it because plumbers are expensive.

The drain blockage is further down the line , after tub and shower drains combine in one common pipe. Use 1/4" or 5/16" x 30' cable, insert it through shower drain and go as far as you can. You will feel the blockage when tip of the cable reaches it. Work that area "back 'n' forth" several times. Have tub faucet run very slowly - just so you can monitor when you penetrate the clog and water level recedes. When unclogged, fill tub with water and drain it all at once. It will flush rest of the debris away. Back to you. Milo

I agree with Milo that the line must be snaked but I would snake from the tubs overflow, (see image) Let me show you how, You have a blockage downstream from the tub. The solution would b e to snake the drain line from the tub overflow. Let me show you how,
Unscrew and remove the overflow plate,(The one with the drain lever) and pull out the tub stopper. You now have a clear shot at the trap. The way you were going in through the drain it ran you square into a tee that you can't get around. Now feed the cable( 1/4" best or 3/3" with a small tip. You can rent a Ridgid K50 sink cable.) About 2' down you will run into the bend of the trap. Crank and push at the same time to work around it. Your blockage will be found in the lateral pipe going to the stack. You shouldn't have to put out more then 10 or 12 feet. I have found tub and shower clogs to be mostly hair and the worm should auger into it and pull it back. After you snake pour a few pans of boiling water down the drain. This will loosen the grease and flush the mess out into the main. Hope this helps and thank you for rating my reply.