It isn't that you want to hold your breath while diving, you never want to close the epiglottis while ascending. When you were doing your CEA or CESA during OW your instructor had you say the 'ahhhhhs' while ascending. This was actually making your keep your epiglottis open.
You absolutely use your lungs to tweak your buoyancy.
More important the breath control for buoyancy is proper weighting, hands down. If you are overweighted, your going to have more air in your BC than your need. As you ascend, and descend for that matter, that extra air is subject to the Boyle's Law, which creates more buoyancy change than is necessary.
When you have your weight correct you'll find that with subtle differences in breathing you can cover a whole range of depths without adding and removing air to your BC.
Once you settle on a depth, you can adjust the air in your BC and then using a relaxed natural breathing style, you'll stay exactly where you want.
As mentioned above, 'shallow breathing' can lead to hypercapnia, or CO2 retention, which can lead to other things.
A way that I've found to really get the feel for what your breathing is doing is to focus and practice hovering is shallow water. Practice hovering at 15 ft, or just off the bottom of the deep end of the pool, or hover mid water in the shallow end of the pool.
Thanks to Boyle's Law, the greatest change in gas volume occurs in the first atmosphere.
As you overbreath or underbreath, you are going to notice the change much more in shallower water. Feedback will be more immediate in shallow water.