Is it necessary to continue checking one's underwear for traces of stool after passing gas, knowing that this inspection causes embarrassment and anxiety, and that traces have only been observed on a few occasions?

After the emission of gas, you are not obligated to inspect your clothes out of fear that some feces may have exited, unless you are certain of its exit. As long as you have not found traces of feces except once after inspection, then this inspection is not required of you. If you become certain that some of it has exited, then it is obligatory to purify whatever it has contaminated of clothing or body. We advise you to turn away from these doubts, as ignoring them is the best remedy for obsessive whispering (waswasah).