There are lots of ways to describe embarrassing situations:
"I didn't know where to hide."
"I have never been so embarrassed."
"Somebody shoot me!"
"I felt very small."
"The roof caved in around me."
"My foot was firmly planted in my mouth" (when saying something very inopportune)
"I really stepped in it this time" (when making a very public mistake)
There are many types of embarrassing situations and different reactions to each.