Hi! I have numerous health conditions and some experiences of discrimination against my own disabilities. I am also a Disabled Students' Officer at City University, so I hope that I can help you in any way that I can.
I can completely understand how you must be feeling. It's really frustrating when university and doctors are not listening to you, they can almost make you feel like it's all in your head. I can tell you that it's absolutely not. I have various health conditions and I had received shocking treatment from both university and previous doctors. Just because someone is in a profession does not mean that they have the authority to take you any less seriously than anybody else.
Change your doctor as soon as you can. I cannot tell you how many doctors I have seen that ended up being totally useless - but this is only because I have a very complicated medical history that not a lot of people understand. But please don't let this put you off.. you would be surprised how easy it can be to find an understanding doctor. Your current doctor is not the right one for you, because it seems to be that he is not taking you seriously enough and it absolutely is not acceptable.
Regarding university, did your tutor explain why the extension was not granted? Under the Equality Act 2010, a disability is defined as a "physical or mental impairment that has a 'substantial' and 'long-term' negative effect on your ability to do normal daily activities.". Provided that you have made the university aware of the difficulties you have to face and further evidence (such as a doctors letter) then it is against the law to deny you any reasonable adjustments. However, I understand that you don't have a doctors letter because he feels your mental issues are not longing. This is why it is so important to change your doctor asap so that you can get a letter. Although, this should not stop the university from providing you temporary adjustments. If your tutor is not understanding, then speak to somebody else within the university and explain your situation. They should provide you this extension for the time being as long as you promise to get the evidence as soon as you can.
If you have any questions about anything, please do not hesitate to give me a message. I will always be happy to help in any way that I can. This is one of the many problems that I am campaigning for.