"....バイト先でお客さんから人気な自分アピールしてくる大学生の店員が聞いてもないのに 「オレのオススメはこれっすねー」とか言ってくるのなんか調子乗ってて....."
I can't find any meanings so thank you if you will help me!
調子に乗る is an expression meaning "to get carried away," "to get caught up in the moment," or a variety of other possible English translations.
Sometimes particles like に are omitted in casual Japanese.