Denise:
The most common rash on the face of a 15-month-old is eczema. Acute eczema looks yellowish and weeps, yet is not infected, which is probably why antibiotics didn't help. Soaps and detergents do not cause eczema, which is an inherited sensitivity. Eczema is superficial and does not scar. Tey qapplying cool compresses with a soft cloth twice daily for 5 minutes, followed by over-the-counter 1% hydrocortisone. Mositurize as needed. If it's much better in 5 days, that will suggest that eczema is present. This may recur, of course, but tends to get milder in later childhood.
Best.
Dr. Rockoff
P.S. Yes, indeed, eczema comes and goes for no reason at all. But you should be able to control it easily. If not, a dermatologist should be able to help.