Can swallowing cause dry sockets after wisdom teeth removal?

Not usually: Dry sockets result from the loss of the blood clot forming in the hole where the tooth was. Anything that will disrupt, dislodge, rupture, loosen or break this apart is to be avoided. Most common is rinsing too soon/hard/often, smoking, eating wrong things / too soon. Swallowing not usually an issue.

Definitely, no: There are certain risks associated with any tooth extraction. The most common complications are infection, dry socket. However, as long as you follow your dentist’s instructions, you should be able to avoid this complication.