Based on my elementary understanding of cooties, he's calling a male buddy of his with whom he shares a G-rated eskimo brother relationship -

If it's a girl on the other line who he presumably kissed in an abashed manner (which led to his goofy grinning for long periods of time directly after until his mom asked him why he was smiling so much), it wouldn't make sense, since the girl already KNOWS she has cooties (even if she denies it like all girls do).

As any young boy knows, ALL girls have cooties, which is why as a precaution you should always get a cootie shot prior to initiating contact with one, no matter how sweet her smile may seem. Even if she shares her jell-o cup with you. And even if she stands up to the school bully for you.

Of course, our boy in question here clearly forgot to circle circle dot dot himself followed by circle circle square squaring to make sure he had it taken care of everywhere. It's unfortunate that he came upon a contagious case of the cooties, since there have been many documented cases of a young lad getting away with a quick peck on the cheek and escaping unharmed.

Luckily, his sense of brotherhood has led him to warn his fellow buddy who, too, has fallen to the amorous charm of this cootie-laden lassie.

That, at least, is the reasonable conclusion I'm drawing from this picture and the accompanying lines of text.