What about being in a seated position? For every exercise that we spend submerged in the pool, we are always seated or on our knees (same for the instructor). Keep in mind, this is a 5 ft deep pool.
The instructor has mentioned how you want to be neutrally buoyant and encouraged us to do so while swimming around the pool, but we haven't really reviewed in depth on how to stay Neutral buoyant/Trim. He has mentioned that we need to practice using our natural breathing to control our buoyancy, but he's never had us try to stay trim or horizontal while performing exercises.
That also is unacceptable. I have gotten my students neutrally buoyant and trim in 4 feet of water. Swimming to maintain depth is a means of masking not having good neutral buoyancy.
I wish to emphasize that one of the signs of a good diver is being still and horizontal, stationary in the water column.
My suggestion for you is to take a course with @Jim Lapenta after you complete your course. He will get you properly weighted. Either that or UTD Essentials (Find an Instructor · UTD Scuba Diving) or GUE fundies (GUE Instructors). Any of these 3 options will be excellent and you will have an amazing time diving afterwards without any struggles.