Clarification regarding grammatical patterns when discussing illnesses

Hello everybody! I’m sorry in advance if the formatting is strange, on mobile yada yada.

I’ve got a quick question regarding grammar when discussing illnesses. I’m already aware that when you have symptoms, such as a cough, a fever or something, it’s as simple as using がある、がでる、が止まらない。

「熱があります」
「鼻水が出ている」
「血が止まらない！」

However, when discussing the suffering of illnesses, such as 花粉症、不眠症、 etc, I’m getting slightly confused about the grammar. I’ve read sentences such as 「私、花粉症ですよ」 which I find confusing. This is in contrast to these sentences;「私、花粉症で苦しむ」
or
「私、花粉症に悩んでいる」which follow the grammatical patterns I’m used to. Ive never seen a noun qualifying noun, and I suppose that’s why I’m confused? So the question really is, how does 「私、花粉症です」 make sense? Is it as simple as a shortening used in colloquial language? 「私、花粉症(に悩んでいる)です」？

I do apologize if there’s a quick answer that’s easily found online, I’ve had a look around but haven’t found anything that has really clicked.