Hi Op,
I was one of the posters who urged you to go to A&E yesterday and reading what's happened since, I'm really glad you did.
I'm really sorry to hear about your double diagnosis. We are 'blessed' with a rich autoimmune history in my family including T1D, Addison's, underactive thyroid, Reynaud's and probably more way back that I'm not aware of.
re: T1D
You will need to start Carbohydrate counting - this will be explained to you. It's not difficult once you get used to it but it might take a while for your insulin ratios to be worked out as from memory things can be a bit up and down in the first few weeks after diagnosis as your body readjusts to having insulin to use again. You can expect a few lows where you can feel shaky and horrible - which maybe won't be that low, but your body by now will be used to having high blood sugar.
Carb counting is basically counting up all the carbs in a meal and injecting the corresponding amount of insulin to balance out the carbs you're eating. It's not an exact science and as time goes on you'll get a good feel for different foods (and have the gift of being able to look at a plate of food and guesstimate the carbs in it). Be aware that fats - eg cream slow down carb absorption. Also look up 'resistant starch' (ie reheating cold starchy (carby) food like potatoes so you don't get a blood sugar spike) It wasn't something we were told about when DS was diagnosed but is really good to know for everyone, not just people with diabetes. There are lots of places to read about T1D and loads of info out there.
re: Addisons
This is a bit more tricky as it's less understood my many endos IMO, but hopefully yours, like ours will be on the ball. I would recommend the Addisons society forum - you can joint for about £30 a year I think (I am a member on behalf of my daughter).
You will be put on tablets - usually hydrocortisone to replace your missing cortisol and fludrocortisone to help you stop losing salt. You can also take prednisolone as an alternative. I would recommend reading up on Circadian Rhythm Dosing and any literature about Addison's by Professor Hindmarsh. There are many documents available online about his work (I think he is a paediatrician, but the same principals apply). There is a really good booklet called Living with Addisons Disease: An owners manual that I also recommend. Addisons really is one of those things where you should educate yourself as much as possible because it's quite rare and often misunderstood.
The other Addisons related thing I would recommend is taking 10-20mg DHEA each day because natural DHEA is mainly made in your adrenal glands and you may find yourself low in oestrogen as a result - it's covered in the booklet I mentioned above. Most importantly when you have Addison's you have to try not to overdo it by burning the candle at both ends because you will feel it more than most people and take longer to recover.
Good luck OP. If you want to ask me anything, even by DM please feel free x