If you find something that may have punctures your tyre, it’s always worth spraying it with soapy water to see if any bubbles are coming out.
Try moving the object side to side, just to give air a chance to escape.
If air escapes leave the object where it is.
If no air is seen, try agitating it more while pulling it out slowly, ensuring that no air is coming out.
Sometimes a screw or object may not be as long as to puncture the tyre.