The use of the contractions there’s , here’s , and where’s with plural nouns is very common in spoken English but is grammatically incorrect, as you suspected.
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phxsunstoonThere is so many fish in the sea. (correct)No. There are so many fish in the sea. 'Fish' is a perfectly acceptable and natural plural form of 'fish' (as 'sheep' is of 'sheep'. 'Fishes' exists, but is less commonly used. You can't say that a word is used non-countably and then use it with 'many'!