However, there's another problem in the sentence you're working with. (And I must say it is such a pleasure to hear that there are other families that argue about grammar!) When the subject and predicate are linked with a linking verb, the predicate takes the nominative form. This is why, when answering the telephone, we might say, "This is she." Your sentence uses a linking verb, "are," and the compound subject, technically, should be in the nominative, "Nick and I." There is a difference, however, between what one ought to use in formal writing and what one actually says and uses in most situations. What does the famous detective say when she finally discovers the body of the murder victim? "That is she!"? I think not. I think she'll blurt out, "That's her!" And that's what will happen in your sentence: most people are going to say and even write "The only people that have colds are Nick and me." Many good writers, in fact, will argue that there is no reason why the linking verb (a "copula," it's sometimes called) cannot link to an object form of the pronoun. The French do that when they say "C'est moi." (Although arguing from the French would be a dangerous thing to do, wouldn't it?) It's an interesting argument and another example of how the language continues to change and evolve. The evolution of English is not happening in the editorial offices of dictionary and textbook publishers; it's happening over your dining room table.

Authority: A University Grammar of English by Randolph Quirk and Sidney Greenbaum. Longman Group: Essex, England. 1993. Used with permission.

Thank you.

I believe it is called a tittle. Please confirm

Thanks