Adjective for 'made of pus' or 'corrupted by pus' or something of something of pus

The word you are looking for is purulent:

consisting of, containing, or discharging pus.
"a purulent discharge"
_{Oxford Dictionaries/Lexico}

It is not an especially common word in general, but it is the medical word for this.

The actual adjective for pus is pussy, with a double s:

[Merriam-Webster]
: full of or resembling pus
// a pussy wound

Note that the pronunciation starts off the same as that of pus itself—as opposed to the pronunciation of the other senses of the word.

Specific context, either through identifying the location or using it alongside another adjective, will also help avoid any confusion (and possibly unfortunate misunderstandings) when it comes to expressing it in written form:

There is a pussy discharge coming from my arm wound.
My cut is producing a yellow and pussy discharge.

Both putrid and putrescent derive from the same root as pus.

Per etymoline, pus is related to the Latin puter (rotten) and putere (to stink). Putrid made its way into English from these same roots in the 15th century in reference to typhus, aka putrid fever. Putrescent was a later addition, coming into English in the 17th century. Both words would carry the sense that the discharge was foul-smelling.

suppurate

from The American Heritage® Dictionary of the English Language, 5th Edition. intransitive verb To form or discharge pus.

https://www.wordnik.com/words/suppurate

"a suppurous discharge"