Keigo form of nouns, adjectives and aru

Hi,

I am having some confusion about the keigo form for nouns and adjectives. I know that you need to add お in front of a noun/adjective to make it sounds polite, but am I supposed to do that for every noun and adjective in a sentence? For example:
病気って、どんな病気でしょう。
じゃあ、かぜかもしれませんね。
How do I fix those two sentences? Is it necessary to remove the "nee" or "yo" at the end?

And also the verb aru. Is it おありになる　or　いらっしゃる？
熱が３９ぐらいあって、せきが出て、体中が痛いと言っていました。
Do I add おin front of 熱 and せき? The ending must be おっしゃっている, right? What if the sentence ends with できる? Would that be changed to なさる or おできになる?

Thanks in advance! :D

No, you don't have to do it for every noun or adjective/verb.

In the first dialogue, I would not change anything even if you were talking about your professor... if at all, I would do:
（先生が）ご病気って、どんな病気でしょう。
Note that if you are talking respectfully about (the professor) being ill, the "being ill" you might want to use a bit of keigo (as it relates to your professor's condition), the rest can simply stay matter-of-fact.

For the second part too, since you are quoting someone, I would just change the last part to おっしゃっていました。

I mean, there are keigo forms for every verb/adjective in that sentence, but if you used all of them the whole sentence would be just too heavy with keigo :)

If you want to know the forms,
熱が39度くらいあって、would be: 熱が39度くらいおありで、

できる would be: おできになる

"Keigo" does not refer to a particular syntactic construct, but rather to a way of speaking, which manifests itself not only through syntax but also vocabulary, intonation, etc. So, strictly speaking, there is no such thing as a "keigo form". You may, instead, be referring to the so-called "honorific" and "humble" forms.