14yrs old brown thick fungus under toenail & dry itchy cracks between toes & peely bottom feet- 5yrs. Took pills & creams dermatologist or podiatrist?

Both good options. Both a dermatologist or a podiarist can help with the problem.
Toenail fungus. Podiatrists see this problem often. There are several other possible causes this could be and an examination and likely some microbiology/fungal cultures are in order based on your description. Check with you pcp or friends/family for a trusted provider - podiatry or dermatology.
Dermatologist. Dermatologist will be far more experienced and better informed than any other practitioner.
Podiatrist. Either the podiatrist or the dermatologist can treat this condition, however, you may have a wider array of options with the podiatrist.
Both are qualify. There are many treatment options for the described symptoms. Either a dermatologist or podiatrists are qualified to treat skin condition of the feet.