I'm not Japanese, but as far as I know 「むぎゅむぎゅ」depicts grabbing something softly. I'm not sure why, but I wasn't able to find it in a dictionary to my surprise.
However, I know of two dictionaries that might be able to help which have entries for onomatopoeia or 擬音語.
Those are Nihon Jiten and Zokugo-dict.