I looked in the Cambridge Dictionary and mess is an uncountable. I wonder why mess is used with 'a'?
He makes a terrible mess when he's cooking.
I look a mess
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What the Cambridge dictionary actually says isn't that it's uncountable, but that it's "S or U", i.e. sometimes it's a singular countable noun, and sometimes it's uncountable.
It doesn't allow for it being plural (which occasionally it is, in real life), so to that extent the dictionary is inaccurate (and sometimes learners' dictionaries exclude rare senses or uses) - but nor does it imply that it's always uncountable.
It is true that is often used as an uncountable noun ("a lot of mess", "some mess", "some more mess", "not very much mess").
It can also be used as a singular countable noun, as both you and Cambridge noted ("making a mess").
Finally, it is occasionally used in the plural.
Oxford Living Dictionaries gives more than a hundred examples of the use of "mess" as a noun, and none of them are of the plural.
Collins Learners' Dictionary divides its definitions of "mess" as a noun into four senses. The first is marked as "singular", the next two as "variable" (meaning sometimes countable and sometimes uncountable), and the fourth as "usually singular".