I know that 'letting baby nurse on one side at a time' is a suggestion when there are oversupply issues, but the key word is 'let.' There is no reason I am aware of to insist baby stay on one side when baby would be happier switching.
As long as baby is gaining well on via breastfeeding there is no reason to be uncertain. Follow babies lead and you will be fine. And yes sometimes baby is not sure what baby wants to do!
Keep being careful about latch and positioning and pay attention to any soreness. That may need attention if it does not resolve soon.