I guess くちゅくちゅ is a sound of a small wet thing(s) stired.
I happend to see a TV ad of a dental care good some years ago (I don't exactly remember what it was). The narrator said "おくち、くちゅくちゅ・・・" as mouth-rinsing.
I guess you found that くちゅくちして in a manga where one character was asking the other for a licking or a soft stiring.

きゅんきゅん may be a variation of an adverb ぎゅうぎゅう. And yes, it means squeezing.