Just speculating here: At certain depths, anything embedded in your skin is basically a tattoo as noted by Oldgrump and UncleNick. Deeper and it may enter your system and be excreted through your liver/kidney functions. Check with your doctor to see if you should be concerned about toxicity. Shallow embeds will sluff off with your natural skin exfoliation. In between those depths and you have a tattoo that is probably as permanent as any inking done by a professional.
Good luck. Glad you are not badly hurt. Thanks for sharing your experience.