This メリメリ is this onomatopoeia, the sound made when a moderately-hard object (wood, leather, etc) is being cracked, ripped or torn. メキメキ is similar. I think what's being torn or broken is obvious from the context. Actually, メリメリ is a common onomatopoeia to describe this type of situation (try googling with メリメリと引き裂く).
メリ子 is not a word I know, and it's much harder to explain. Perhaps some peculiar wordplay is happening. 子 is commonly used in a girl's name, and 子/こ is also used as a diminutive (e.g., 判子, わんこ). In addition, こ is occasionally used to make a bit cuter variation of an onomatopoeic/mimetic word (e.g., ぴょんぴょん → ぴょんこぴょんこ, ピッピッ → ピコピコ). So, although メリ子メリ子 is probably a made-up word, it is working as a funny expression used to describe what's happening to this girl.