I sprained my ankle on the stairs and the next morning it hurt worse. is this normal? there's swelling on the outer side and font of the foot and ankle some bruising?

It is not feasible to exclude a fracture without examining you and may be taking an X-ray. The swelling and bruise are a cause for concern and it would be prudent to see a doctor or go to an ER, Wish you good health!

Yes: Sometimes pain can be worse after rest. You need to have the ankle checked for a possible Fracture or Ligament tear.

Those are signs of possible torn ligament or an avulsion fracture of the ankle. This degree of sprain must be taken care of properly to avoid chronic ankle problems going forward. I recommend seeing an orthopedic surgeon for best diagnosis, care & follow-up. I hope you're using crutches, apply cold compresses,elevating that leg while sitting in the meantime.