I have a really sore lower back thinking it was muscular i have taken 3 days of antiinflammatories and no relief.

Exercise. : New guidelines for the management of lower back pains further support exercise for the relief of lower back pains.

Evaluate PT: New recommendations from the ACP are to use physical therapies (e.g. exercise, pilates, yoga etc.) to treat subacute or acute lower back pain rather than pain medications. You might consider this option and ask your physician to refer you to a physical therapist or exercise professional who has health care related experience in back pain. https://www.medicalnewsbulletin.com/new-guidelines-lower

Might be : Muscular back pain can still be sore but particularly if not caused by an injury or worsening having the back examined by someone is a good idea. Unfortunately if it does turn out to be muscular you may not be able to get 100% on top of it with medications so may need to consider physiotherapy etc

Sore back: If NSAIDs are not working you may need to see a GP and then review with a physio.

Back pain : Most common cause of back pain is muscles being pulled but there can be other causes too like urine infection , vaginal or cervical infection . If your pain is not improving or you have high fever or numbness in legs or in pelvic area or loss of control over stool or urine then please see doctor .

Strain?: If you can remember lifting something heavy or bending in the hours/day preceding the pain then it very likely is muscular. 40% of this kind of back pain is better within a week & the next 50% takes up to 6 weeks which leaves an unlucky 10% which takes longer still. Pain relief/anti-inflammatories often don't get rid of the pain but just make it a bit more tolerable while you body recovers.