What can happen if a pregnant person get stung by a wasp?

Same as not pregnant: The wasp sting will not affect the fetus. If the mother has a severe allergic reaction, such as anaphylaxis, where the mother is critically ill, the fetus can also suffer from lack of circulation. Otherwise, it is not an issue.

Discomfort: Unless allergic to bee stings the wasp sting venom should not affect a pregnancy. A bee sting allergy would affect the pregnancy by affecting the mother depending on how severe is her allergic reaction.