Hello. Thank you for coming to JustAnswer with your question, and welcome.
The symptoms you are describing sound like a salivary gland inflammation or infection. This could be unrelated to your recent cold, and would have nothing to do with the flu vaccine you received.
Salivary gland infections can be caused by a virus (like mumps), or bacteria. Often the initial cause is a obstruction of the ducts by stones or thick saliva when a person is dehydrated. If self-care at home measures do not result in some resolution within a couple of days, you may need to see your doctor to be evaluated for the possible need of an antibiotic.
Self-care is warm salt water rinses as frequently as you need, but at least twice a day. Use a cup of very warm water with 1/2 to 1 teaspoon of salt. This can be soothing, and may help to unblock the duct if it is obstructed. Also careful massage with heat can help.
If it gets worse, (more swollen, more red, more painful, draining blood and/or pus) you should call your doctor right away. The opening of the gland is low on the inside of your cheek, you can see if anything is draining by gently massaging from the outside and looking in a mirror. Also, if it gets no better after a couple of days, you should see your doctor.
Here is a link that explains further: Salivary gland infection