I have a lump in my right breast. How can I get help quickly and not wait in a long line for a mammogram?

See a breast surgeon. I would not recommend a mammogram for a 28 yr old women. I advise you to see a breast surgeon (ideally one who performs ultrasound). They can assess the significance of this lump and decide what, if anything, needs to be done. In my practice we will see people asap under these circumstances due to the anxiety inherent with this problem.
If doctor calls. If you have new breast masses, you should have the mammogram +/- breast ultrasounds asap. Ask your physician to call the mammogram center to see if s/he can get you in sooner. Also, ask the mammography unit to put you on their wait lists in case any one cancels. I would also recommend seeing a breast surgeon for evaluation as well.
Call the center. You will need a diagnostic mammogram and ultrasound which are scheduled separate at most centers from screening mammogram. The center will be able to make an appointment for you though you do need an order from your primary doc and the center may be able to facilitate obtaining that paperwork.
Lump. Call your doctor and get evaluated. Chances are you will get a script or appointment for a mammogram as well. If you have a lump, most facilities can probably get you in within a few days. Mammography is generally not considered to be an emergency service, so urgent care centers and most Emergency Rooms probably won't have the service available.
See your Doc ASAP. Your Doc can expedite your mammogram and/or biopsy if clinically needed. Call ASAP and follow their lead. Good luck. .