Are you 100% sure that the comma after yes was in the original quote? If you are, how do you know that the second comma was not? Of course, do whatever you like. Generally we separate the speaker from the spoken words with a comma. That is why we say, He said, "Yes, I feel similarly." In that case, though, the comma is outside of the quotation marks and, thus, not breaking your self-imposed rule.
So I ain't a writer by any training, but I was under the impression that quotations of the spoken word followed a separate grammar. That grammar is designed to capture details of how the person said something. For example, "Yes, I feel similarly" (and here I follow @goobster's rule) conveys that the speaker said it in a way that separated "Yes" and "I feel similarly". Two ways that could have happened are with a pause or by raising the pitch of "I". Meanwhile "Yes I feel similarly" conveys that speaker spoke in a monotone, or in a breathless rush of words.