I very much doubt you have developed a fungus. A rash, perhaps. Why do you think it's a fungus?
Here's the info directly from the Rogaine site:
“If you experience any of the following serious side effects, stop using minoxidil topical (the active ingredient contained in Rogaine) and seek emergency medical attention: an allergic reaction (difficulty breathing; closing of the throat; swelling of the lips, tongue, or face; or hives); chest pain; irregular or very fast heartbeats; dizziness or lightheadedness; or
fainting.
Continue to use minoxidil topical and talk to your doctor when it is convenient if you experience
itching, redness, dryness, or flaking of the scalp;”
Rogaine Side Effects | Drugs.com
This is a subject "we" covered in a Pharmaceutical training course. A rash/irritation after several months is NOT uncommon. You can also ask your Pharmacist.