Walk ins only

The clinic that I was going to has recently changed their policy from appointments to only walk in. I have a issue with not having a set time to be somewhere. Especially since walk ins don't guarantee that I'll be able to see the same person or how long of a time frame I'll be there. Those factors make it highly uncomfortable for me. Especially since we don't currently have a car so I have to use medical transportation and so having an unknown wait time is very unsettling. Anyone got any ideas for any ways of coping with them transferring to walk ins?