App or Flow for Room Scheduling

Hello all.  I work for a retreat house and we need some help with automating room assignments when retreatants register.

The basic functionality we need is

1. Obviously rooms should not be double-booked
2. Booked based on type (private room, 2-bed room, larger cottage, etc)

But we have a special consideration:

• A 2-bed room is often converted to a private when we run out of privates.  We do not charge for 2 privates - we just charge the private rate.

I am not sure if I need a full app or if there are some flows that exist out there.  (Definitely looking for free or low-cost solutions as money is tight.)

Admittedly, my flow creation skills are unimpressive!  I'm comfortable with creating record-based action flows like for emails and tasks, but beyond that I'm a total noob.

Does anyone here have any recommended solutions for this sort of resource scheduling / booking?