I am so sorry you are going through all of this. Your symptoms are classic hypothyroidism. I've been there myself and I know how terrible it is and how beyond the physical, the mental fatigue and difficulty concentrating can be so frustrating. I think that the symptoms could have been coming on for some time, you just didn't notice the minor ones until it all came down on you at once. Also, some people (like myself) are very sensitive to small fluctuation in thyroid hormone levels. Just a few days off of my medication (when I had to have a thyroid scan after thyroid cancer treatment--I have actually had my whole thyroid removed, so I'm totally dependent on the meds), I felt really tired and achy. Also, it is possible that the combination of this and your diabetes is making you feel worse faster, I don't know. Is this throwing your blood sugar off or anything?
I think that what ever you have to do to get a test and get the meds you need, you should do it. If you can't walk to the city, get a cab, take the bus, or get a friend to drive you. I don't think that going into A&E would be a bad idea if you don't have any other options. If a regular doctor won't see you, what are you supposed to do? You can't go on like this. It will get worse. And it's going to take time for the meds to kick in. The longer you wait, the worse it will be. Plus, you are a diabetic that has another medical condition coming on. If they treat you like you're wasting their time, they are idiots.
Also, don't avoid your friends and your boyfriend. These are the people you should be able to depend on right now. You wouldn't want them avoiding you if they were in the same position, would you? Wouldn't you want to help them and be there for them? Bring them dinner and things like that?
I hope you get the help you need soon. Once you get on the proper dose of thyroid hormone, you'll feel a lot better. And trust me, hypothyroidism is a heck of a lot easier to manage than diabetes (my husband is a type 1, too), so you go this in the bag.
Feel free to re-post if you need anything else or if you have more questions. Best of luck. Feel better soon.