Just read the first page of the Maltese Falcon, and he writes it simply a lower-case letter without quotes.
So: "I looked like an a."
The letter Hammett uses is a
v, which is not also a valid English word, so there is no chance for misreading it as anything other than a letter.
A does not have that luxury. (This is sometimes true of
i and
o as well.) Also, Hammett is using the letter as a shape, not as a letter, so the context is not the same as yours.
In your original sample sentence, "It's a letter A," there is little chance of misreading, because the phrase "a letter" tips the reader off that what's coming is a letter, and the capital A further sets it off, since the word "a" would not be capitalized at that point in a sentence. In your sample quoted above, "an a" is not a valid use of two indefinite articles, so that also hints to the reader that the second
a is not functioning as a word, but as a letter. Capitalizing it there would make it even clearer.
That said, however, style guides base their rules on wider ranges of problems, such as a sentence like "I is over there," which someone might say while pointing to a file cabinet. That sentence invites misreading, and needs something to set off the initial
i to distinguish it from the pronoun. Thus a style guide will tell you to put such letters in italics or single quotes.
Even if it's not an issue in the particular sentences you've quoted here, you want to maintain a consistent style if you have other sentences where parsing is trickier, so it's best to just have a policy of setting such letters off somehow. Italics is probably cleaner than quotation marks, especially if this comes up a lot in dialogue--which would otherwise require single quotes within double quotes--but either system will clarify the meaning.