1- Painkillers and rest are not your best options
The reason why i said that because you don't have to mask the pain or hide it but you have to treat it.
2- You will go to the ER then go home after having x-ray and do nothing about it
There is nothing wrong in going to the ER to be checked out but that's not it you have to treat your ankle with all due respect to the ER doctors but they are there to rule out serious patholigies or for immediate medical interfere NOT ANKLE SPRAIN EXPERTS.
3- The best thing to do after going to the ER if you decided to go is to see a physical therapist
The reason why you should see a PT is because physical therapists are the movement experts who know how to control your pain and swelling the rehabilitate your ankle to be stronger and then do prevention programs from further injuries in the ankle.
I see everyday patients started with a very small sprain and they ignored it for years and they said to themselves it's just a twinge i will take an overcounter and will be fine but they ended up with more problems that they thought the will have