I'm a 60 yr old female and3 days ago my lower back just started hurting. I'm very active and had lifted some tables and boxes the day before but had not felt any pain.the pain is not going down my legs and mostly hurts when I move suddenly or in certain ways. What can it be?

You need to do the r. I. c. e.

The R.I.C.E. Method of Acute Injury Treatment
•Rest: Resting is important immediately after injury for two reasons. First, rest is vital to protect the injured muscle, tendon, ligament or other tissue from further injury. Second, your body needs to rest so it has the energy it needs to heal itself most effectively.
•Ice: Use ice bags, cold packs or even a bag of frozen peas wrapped in a thin towel to provide cold to the injured area. Cold can provide short-term pain relief. It also limits swelling by reducing blood flow to the injured area. Keep in mind, though, that you should never leave ice on an injury for more than 15-20 minutes at a time. Longer exposure can damage your skin. The best rule is to apply cold compresses for 15 minutes and then leave them off for at least 20 minutes. (Read The Proper Use of ICE).
•Compression: Compression limits swelling, which slows down healing. Some people notice pain relief from compression as well. An easy way to compress the area of the injury is to wrap an ACE bandage over it. If you feel throbbing, or if the wrap just feels too tight, remove the bandage and re-wrap the area so the bandage is a little looser.
•Elevation: Elevating an injury reduces swelling. It's most effective when the injured area is raised above the level of the heart. For example, if you injure an ankle, try lying on your bed with your foot propped on one or two pillows.
After a day or two of R.I.C.E. many sprains, strains or other injuries will begin to heal. But if your pain or swelling does not decrease after 48 hours, make an appointment to see your primary care physician or go to the emergency room, depending upon the severity of your symptoms.
RICE - Rest, Ice, Compression and Elevation Best Treatment for Acute Injuries