Do not try drano or liquid plumber. You have a major clog in a major pipe for it to be doing this. Bite the bullet and call a reputable plumber to resolve this issue. You may have to have a section of pipe replaced.
Try boiling water. Let the tub drain as much as possible & do not use the sink. Carefully carry & pour a closed kettle of boiling water (no open cook pots!) down the drain. This melts soap & conditioner build-up & helps release hair clogs. It may take 2-3 attempts. Or, it may only be a small amount of hair blocking the tub stopper trap. Check this first. Pull the stopper up & use a pair of tweezers to probe & remove any hair tangled in the trap's small drain holes & crevices. (This happens often with my tub drain.) If still a problem, Draino or Liquid Plummer should do. But ideally, purchase a drain snake. This will probably happen again & its dangerous to handle these chemicals & allow them into the environment.