Forget baking soda and vinegar: when your drain is clogged, most of the time it is filled up with a hair ball and other miscellany. Ewww. You need to get that junk out BEFORE you clean the drain with baking soda and vinegar. I bought the Cobra Zip-It Drain Cleaning Tool, and I have used it for years on my sink and shower drains.
You just stick it down the drain, and the little nubs pull the hair back up. THEN you clean with baking soda and vinegar. I will spare you photos of me cleaning out my drain because I think you get the idea. If you need to see the filth or a demonstration, you can go to the Zip-It website and see what other people pull out of their drains.
This little guy rocks.