Thanks for the query,
You are correct,
You might have developed Athlete's foot which is a fungal infection
The dark patches may be due to post inflammatory hyperpigmentation
These are common after any type of infection.
Please get a KOH mount done,
This can confirm the fungal etiology.
Treatment can be with oral antifungals as well as with topical antifungals.
Please meet a dermatologist
for exact diagnosis.
Let me know if you have any other doubt.
you can ask a direct question to me on this forum, following the below link.
Wishing you a good health.