I live in the UK, I have dealt with GPs and can quite bluntly say for the most part they don't know enough to assess / support / criticise your situation because they are not trained do so. General Practitioner, suggests to me jack of all trades master of none.. If you are unhappy with the support a doctor gives, complain and get another, repeat until you find a doctor that you can connect with and feel has a real tangible understanding of your situation. When in a time of crisis, it doesn't take a lot to make a person crumble, I think it is normal to become disheartened by what you described.. Just have to remind yourself that only you know what you are going through right now and no matter what form of communication you use there will be a severe lack of understanding by the recipient - unless that person has experienced this too.
As for trying to understand communication from other people, I have been learning British Sign Language since January this year and about to take my first exam, BSL 101..
One of the main things I have noticed is how much information is lost during lip reading, my teacher is profoundly deaf and has been his entire life, he is a master at reading people's signals but still has to reconstruct what you say while he is lip reading because quite frankly there is too many words that look the same. I saw a statistic online that only about 30% of what a person is saying can be detected by an excellent lip reader, sobering I think.
Also in case it hasn't been told to you, background noise will effect your hearing, that is normal - that in itself demonstrates that the Doctor doesn't understand deafness... Besides, I can't help but wonder if you would benefit from exposure to the Deaf culture - I am hearing and have been treated kindly by several Deaf people at the Deaf pub. I met a man who was able to lipread astonishingly well, which put me at ease as at the time I could barely express anything I was thinking through sign language.. I still am a beginner obviously, but after a few months I can have some conversations with Deaf.
Besides, I think sign language is a beautiful language, it feels incredible and has opened me up to see signals from hearing people as they communicate that I hadn't noticed before.