If a foreign body of any sort was trapped under the skin, would I notice? Would there be some kind of response or reaction?

Maybe. Hi, Thank you for your question. Your body would usually create a barrier around the foreign object to prevent it from being absorbed into your body. You might have pain, swelling and redness in that area initially. Hope that helps..contact me if you have any other questions :-) Dr. M.
Foreign body. If there is a foreign body under the skin it will present with discomfort, swelling, redness or inflammation or drainage.