What's the best treatment for a mild knee sprain and slight inflammation on the inner side?

Treatment: Ice for 20 minutes, three to four times per day. You could wear a hinged knee brace for support. Only use crutches if you really need to. Take an over the counter anti-inflammatory if you can.
"R.I.C.E." Sprains are best treated with rest, ice, compression, and elevation. Inner knee pain can be a sign of a mcl (medial collateral ligament) sprain, which tends to do well with conservative non-surgical care. Persistent pain can be a sign of a torn medial meniscus, the shock absorber of the knee, so any knee pain lasting more than a month to 6 weeks should be checked out with an orthopedic surgeon.