I fell on my elbow on concrete 6 weeks ago and it is still tender to touch but ok to move. should i get an x-ray?

If worried: if you can move the joint after 6 weeks you could have had a non-displaced fracture that is healing and there is not much they will do. If the movement is decreased any see your physician and get an X-ray

Possibly yes: Usually it takes time for an elbow contusion (bone bruise) to feel better after a direct blow because there is very little padding between skin and bone. If there is no sign of an obvious break in the bone after initial injury , usually ice and motrin/aleve will help. If not better after 2 weeks, an xray would help to find a small fracture. So after 6 weeks and not better. Xray may need to be done