You may feel some discomfort and swelling for a few weeks after a deep cleaning. Depending on the extent of the infection, it may take a while for the symptoms to go away.
In the meantime, you can take over-the-counter medications to help with the discomfort and pain. In addition to the post-care instructions, your dentist recommends rinsing your mouth with warm salt water to keep your mouth free from bacteria and heal your gums.