Are any of the places doing walk-ins?
There's a lot of places doing them now. We got our initial series as part of a weekly mass clinic through a hospital but they aren't doing boosters this way. But many other places are from Walmart to CVS to Walgreens, etc. At least online Walmart wasn't doing appointments but rather walk-ins. Not sure if that's still the case.
I do know something that has been happening in my area is pharmacy staff shortages causes places to cancel their appointments when they don't have staff to administer the shot and at times (but doesn't seem to be a wide-spread issue) not getting in their supply at that time.
We did our flu shot as a walk up in a CVS in a Target, we did our booster as an appointment in a CVS near our house.