Yikes yeah that does kind of sound like it. I'm sorry you had to experience that. It's a shitty disease.
I developed a pretty bad ulcer on the inside of my cheek. It was super inflamed and my upper teeth rubbed it whenever they moved, causing quite a bit of discomfort. In retrospect it was probably just a bad apthuous ulcer (canker sore) but it didn't have the typical look of one, nor do I typically get them.
The kicker was that I was taking a course of Meloxicam, which is an anti inflammatory medication which is very much linked to SJS, so I panicked.
I work in critical care and have seen a lot of bad SJS/TEN (toxic epidermal necrolysis) cases and my mind immediately jumped to those. I've seen every inch of skin fall off of people.
Medical people are the worst hypochondriacs lol.
I think the first decision to make is pre built vs DIY. The most common pre built solution would be something like Synology. You may start researching there and see if that would fit your needs, or what people do as alternatives.
I personally built one with a similar use case and use Unraid for my OS. The other normal option is TrueNAS.
With that budget you'll be able to get a good result.