You need to know two measurements when choosing a bra, both taken by measuring all the way round your body:
Your exact measurement under your bosom and your measurement at the highest point of your bosom.
Next when looking for bras, make sure you have your reading glasses and/or a magnifying glass with you and check what the elastic is made of. This should be included in the specifications on the label as to what the bra is made of.
If like me, you are allergic to polyester then the sewing thread may be causing the problem, or the elastic may contain polyester.
You could try covering the elastic on the bras you have that are not too tight with pure cotton tape sewn securely so it entirely covers the elastic.
Another solution is to buy or sew some very thin chemises, preferably in pure silk and wear them under your bra. This lessens the irritation caused by elastic, hooks and eyes, sewing thread etc.
Burda used to make sewing patterns for underskirts, chemises and french knickers and probably still do - I just use the pattern I have.
Some shops do still stock pure cotton bras, but you will need to google these, as I don't live in the UK or buy clothes there, so I can't help with a stockist.