I have never been professionally fitted, but I have the same concerns. I am 40 under and 45 bust, which comes out to an E cup. Not even close. I wear a 40B comfortably.
The issue is that standard sizes are estimates of volume. Then different manufacturers have their own sizing recommendations that also don't work. Part of the problem is that AMAB breasts sit differently on the chest (farther apart), torso (rib cage) dimensions are larger regardless of breast volume, and these throw the whole formula out of whack.
In my opinion, a professional fitting CAN be useful, but if they are looking at my Bs and recommending Es, that is not helpful. I have purchased various sizes of band/cup combinations and found what works.
If the band is digging in, you need a bigger band, so drop a cup size to keep the band/cup ratio similar. Check out Sister Sizes for how that works. Look into Warner brand bras. I have a few, and they are very soft and comfy, with a nice side panel that helps prevent side discomfort. This could also help with side spillage.
This is just my experience.