Is there a word for relieved happiness? Like having experienced trauma, and now feeling happy from relief

"They were covered in dirt, acne, and _____ all over."

First, "all over" is redundant; the word "covered" already implies "all over." I would recommend nixing "all over." This change would free up how you could finish the sentence though. It would make it easier for you to put a phrase rather than a single word.

"They were covered in dirt, acne, and _____ ."

• giddy disbelief
• relief
• etc.

Because you use the verb "covered," you limit yourself to the words you could literally use. You're looking for an emotion word, but you can't literally be covered in an emotion (like you can with dirt and acne). I think it's still fine though. You can try switching the verb though to open up some different options; you could also try ascribing a new verb to each item in your list: covered in dirt, overwhelmed by acne, and incredibly thankful to finally be safe.