You are not "too old", but your symptoms should be investigated with your doctor to get to the cause. It may very well be mostly do to your furniture moving of eight months ago and whatever popped in your lower back, but then it could be something else.
The inner thigh muscle is also called the adductor muscle, and it is primarily responsible for turning the toe in while walking or running. It is possible to pull or injure the upper inner thigh or the lower inner thigh while performing different exercises or to simply overwork the muscle by running, hiking or playing sports past the point of fatigue or tensing the muscle to avoid slipping while running or walking on wet surfaces.
One of several causes of inner thigh pain may be due to a groin strain or a groin pull. This often happens to runners and those who play sports -- such as soccer or tennis -- that involve a great deal of running. The inner thigh pain can be mild, caused by a small strain of muscles that connect the thigh bone to the pubic bone. Inner thigh pain can also be moderate to severe, caused by a total rupture of those same muscles. Additionally, you may experience pain on the outside of the inner thigh due to rash caused by the friction of the thighs rubbing together while running on a treadmill or outside.
I suggest seeing a doctor of Osteopathic Medicine (D.O.)
Don't give up, just slow down a tad.
You can work out at the gym at nearly any age. You may have to substitute jogging/wogging for quickness and speed. But don't quit.