Yes, this could be arthritis... or synovitis (inflammation of the lining of the joint) or tendinitis (inflammation of the tendons). And certainly may be related to activity.
Running is hard on the lower limb joints especially without pre conditioning. I recommend at least 3 months of strengthening and low impact cardiovascular training before attempt any serious running. Stretching is also important.
If this pain is persistent, then an x-ray and a visit to your physician may help find an accurate diagnosis.
Tom Plamondon PA-C, PT