There is no single gene for Multiple Sclerosis, or (that I know of) type 1 diabetes.
At least 60 genes have so far been discovered that influence lifetime risk of MS, but even having all of them does not mean someone will certainly get it. That’s why it’s not considered a hereditary disease - there’s no single gene that always causes it, and can be passed on.
As I understand it, people with MS are slightly more likely to have type 1 diabetes, and vice versa, and they are more common in the same families, indicating there may be shared genetic risk factors. But already having type 1 diabetes is not used to inform an MS diagnosis in any way. The overlap is not significant enough to say that if you have one, it’s a deciding factor in whether you also have the other. The diagnostic criteria for MS don’t look at other diseases you have at all (unless there is a possibility they could be causing your symptoms, in which case they have to be ruled out). The relationship is nothing like as straightforward as having one making it “obvious” you have the other. It’s just a slightly increased risk factor, that’s all.
I could be wrong, and you are in fact diagnosed very quickly (but not on the basis of the diabetes). Some people get a very fast diagnosis. However, I wanted you to be aware it’s the exception, not the rule. For most people, diagnosis is quite a long-drawn out process, and even “textbook” MRI findings are not usually enough by themselves. It must be proved they couldn’t be the result of a single incident. The technical term is “dissemination in time” if you want to explore it in more depth on Google. Together, the MS diagnostic criteria are called the Macdonald Criteria. I hope I’ve spelt that right - I can never remember if it’s Mc or Mac, but I think it’s Mac (50-50 chance).