A term for someone denying an accusation but appearing guilty as a result
In this example, you might be protesting too much.
Shakespeare introduced the phrase in Hamlet: "the lady doth protest too much, methinks".
"The lady doth protest too much, methinks" is a quotation from the 1602 play Hamlet by William Shakespeare. It has been used as a figure of speech, in various phrasings, to indicate that a person's overly frequent or vehement attempts to convince others of something have ironically helped to convince others that the opposite is true, by making the person look insincere and defensive. (Wikipedia)
The phrase can mean the denial/protest is too frequently repeated but it can also just be due to the vehemence or phrasing of the denial. It can be thought of — as the Wikipedia article on the line in Hamlet says — a subtle, unintentional apophasis.
Apophasis is a rhetorical device wherein the speaker or writer brings up a subject by either denying it, or denying that it should be brought up. (Wikipedia)
A single misplaced word can cause others to think the person protests too much.
Accusing someone of protesting too much is a not-so-subtle form of double bind. To deny it is to protest even more.