As a mom with a daughter in college who was recently diagnosed with ADHD and with a midschooler with dysgraphia, I think you're right that the most pressing issue isn't the diagnosis but finding work-arounds and accommodations to help your daughter succeed. The diagnosis can come later when she's home for winter break or summer.
Since she can articulate what she wants to say but has anxiety when she has to write it, is there someone, maybe even another student, who would be willing to type while she dictates? Perhaps she could offer a trade of some sort - doing a favor in return for theirs. Another option is to try out Dragon Dictation. It does pretty well with predictive text. She'll likely need need help editing if she's poor at spelling, but she can email it to you for that if you can help with that part. And the last option is for her to record herself dictating the paper and then type it out as she plays it back.
Hope this helps.
