Pokemon is both singular and plural, right?

You are correct. "Pokémon" can be used as a singular and plural noun. In the National Pokedex from the Pokemon Database, the following information is provided to users.

This is the complete National Pokédex for Generation 7, which lists every one of the 807 Pokémon discovered so far.
Click a Pokémon's name to see its detailed Pokédex page, or click a type to see other Pokémon of the same type.

The listed number of 807 alerts readers to the fact that the "Pokémon" word that follows is not being used in the singular form. Replace "Pokémon" with "dog" and the sentence doesn't make sense. The second sentence uses the singular version of the word, as identified by the usage of the indefinite article "a" preceding "Pokémon's." While it is rare to find a word that is both singular and plural, it is not completely unheard of. "Sheep," "aircraft," "salmon," "trout," "offspring," "species," "fish," and "moose" are all other words that function as singular and plural.
https://pokemondb.net/pokedex/national

Pokemon can be used as both a singular and plural word.
The lyrics to the intro song of the popular cartoon "Pokemon" states:

Pokemon, gotta catch 'em all

By using "'em," a shortened version of "them," we can conclude that Pokemon is suitable to be used in the plural form. You could say "I have many Pokemon" or "look at all of those Pokemon." Both would be correct.
You would not say "I have many Pokemons." Adding an "s" onto the end would be incorrect.
Pokemon can also be used in the singular case. Within the playable game there is near-constant dialogue. Within those text boxes we can clearly see the word Pokemon used in both singular and plural forms. For example:

Oh! What's this? A rare Pokemon!

By using the word "a" instead of a word that would reflect a plural, such as "some," we can see Pokemon being used in its singular form. You could say "This is my Pokemon" or "I have a Pokemon." Both would be correct.
Feel free to use the word Pokemon in both singular and plural forms—just remember not to ever add an "s" for the plural form.