Painless small hard lump posterior axila normal mammogram did not show it at all would you recommend biopsy or further testing?

Both: Not all mammograms can get high enough in the axilla to see it. For just such instances i recommend ultrasound . It can give you a lot of information. Don't delay. See your doctor.

Further Evaluation: If the mammogram was unable to demonstrate a palpable mass then it has not been evaluated. Further workup is appropriate. An ultrasound would be a good next step to determine the characteristics of the finding and possibly aspiration or needle biopsy guidance. The lump should not be ignored!

Probably: ultrasound, and then biopsy if it looks suspicious.