Oh OP, I really feel for you! What an amazing job you've done to keep going through that. People think they're being helpful saying you should just stop but actually I needed people to say that I could carry on even though it was so hard and painful.
I too had a difficult start to breastfeeding with 8 weeks of terrible pain from a tongue tie and mastitis. My DD is now nearly 2 and we are still going and no plans to stop any time soon. However, for a few months recently I was struggling with mastitis and milk blebs again. So over the last couple of years have done a shed load of research into this that may help you!
First, are you aware of the Academy of Breastfeeding Medicine protocols? They updated their mastitis spectrum one in 2022 and the advice is v different to standard GP/NHS advice i.e. ice, antiinflammatories, v gentle lymphatic massage NOT heat, vibration, deep massage.
https://www.bfmed.org/protocols - number 36.
I kept many flare ups at bay without needing antibiotics (though had antibiotics the first time and then again in January when I was very run down) by following this advice. This is your first aid effectively.
Now in terms of root cause, can you see someone properly trained in tongue ties? (Midwives, health visitors and GPs are not.)That is a common cause of mastitis because the milk transfer isn't effective enough. There are good tongue tie practitioners and bad ones, we unfortunately saw a bad one and as a result my DD is still restricted, hence ongoing issues. It's really important that the practioner works by not jumping to a release straight away, instead solving tension issues first so that the release can be effective. They also need to follow up with you afterwards. I recommend Faye at Rockabye Hub in Chester or Kellie at Pitter Patter Tots in St Helen's.
Then there are also things you could try for longer term prevention. I also now take 10g of soya lecithin a day and that seems to stop me getting milk blebs. When I tried to taper I started getting symptoms again straight away. I also take ligilactobacillus salivarius probiotics (not so sure about the effectiveness of that). These are both mentioned in the ABM protocol I linked.
To answer your original question about doctors trained in lactation and who are also medical, I found two: Sharon Silberstein in London https://www.instagram.com/breastfeedingdoctor.uk?igsh=ZDlzMW5xcXpjeWV6
and Justice Reilly in Scotland https://www.instagram.com/breastmed?igsh=ZjB1Y2l2ejhjMHg3 .
I didn't end up seeing them as my symptoms eased and I saw Kellie about the tongue tie instead.
More than happy to talk more about this - it's a subject I feel super passionate about and so angry about how poor the support is. A lot of the things I've suggested cost money and it breaks my heart that many people will not have the privilege to access it and are just given misinformation.