You can get lead poisoning from birdshot if the birdshot you were shot with was made from lead.
Some birdshot is made from steel while other birdshot is made from lead and if you got the lead type of birdshot inside you then you may get lead poisoning.
However sometimes birdshot is left inside some people by doctors because of a more severe risk of causing further health issues or injury.
Most times the birdshot left in someone won't cause lead poisoning.
But it's best to avoid getting shot by birdshot or avoid getting shot in the first place.
Now if you eat the birdshot then yes you could get lead poisoning if you ate the lead based birdshot.
Or if you swallow any type of lead then it can lead to lead poisoning.
When someone gets shot with pellets or birdshot or other bullets sometimes doctors will routinely leave pellets or bullets in the body because the risks of surgery are deemed greater then the possibility of the lead poisoning.