The method I use for my bra fitting is as follows:
Measure under your boobs, that is your basic band size. Then with no bra, measure across your nipples. If the answer is 1" bigger, you are an A, if 2" bigger, a B and so on. That's only the start, though.
Now go on eBay and order a couple of cheap bras to your nominal size (but not ones from China, cup sizes too small). Better to bid for used bras from well known makes like M&S or Victorias Secret. Used bras can be bid for very cheaply.
When they come, assess whether they fit well or not. After a couple of tries you will establish your size with reference to a principal supplier and off you go.
A new brassiere may well feel firm on first wearing, but my "go to" bras were always a bit too tight to start with.
When in doubt, I go for the larger cup size with padding, as I can always use chicken fillets and nipple pumps to advantage.
Unsuitable bras can go to the Salvation Army.