The wrong position of a comma

"Since we're in class, I would like to share with you something I learned just recently. Little lesson which is, people may care about people who care about themselves, but I just don't really care about those people."

I don't think the sentence above is idiomatic as it is, but think if the comma after "is" is shift before "which" it is idiomatic.
So I'd like to hear about your opinion.
Thank you in advance for your help.