The shortened diphthongs on “I” and “”my” are optional and vary regionally. The “t” at the end of “put” changes because of the following /m/ sound. Pronounce the “t” with both lips, but keep them closed, pause, then make the /m/. You’ll need to practice.
This means “I think I said something wrong”, maybe you’ve offended someone, or let somebody’s secret out. If you’re wondering what you put your foot in, we also say, “I put my foot in my mouth”, so there’s your answer.