This would have been an excellent question to ask starting in August, when shots first became available.

Your lack of planning doesn't constitute an emergency.

and also says this about the flu shot specifically -

"Seasonal Influenza Vaccine
This influenza season, children 6 months through 18 years, certain high-risk adults 19 through 49 years, and adults 50 years and older who are enrolled in new group and individual health plans will be eligible to receive the seasonal flu vaccine without cost-sharing when provided by an in-network provider. Beginning in the plan year that starts after March 2, 2011, all adults 19-49 years of age will be eligible to receive the seasonal flu vaccine with no cost-sharing requirements when provided by an in-network provider.
"

http://www.healthcare.gov/news/factsheets/2010/07/preventive-services-list.html#CoveredPreventiveServicesforAdults

this website says that flu shots are free under a network provider for insured individuals -

Immunization Services for Adults
adults covered are
"Adults 19 years and older who are enrolled in new group or individual private health plans will be eligible to receive vaccines recommended by the ACIP prior to September 2009 without any cost-sharing requirements when provided by an in-network provider as of September 23, 2010.

"

A little harsh, people. We don't know OP's financial situation - she could be going through a hard time right now. That being said, I can't imagine any insurance plan not covering the flu shot - seems impossible. I would double-check, OP.

Nothing is ever "free". What you are proposing is someone else's tax money be redistributed to you in the form of flu shots so that you do not have to pay. The "government" cannot provide anything for free. They simply tax and spend. Be a responsible adult and pay for your own damn flu shot.