I have a painful lump under skin on bicep/ elbow. Hard lump not visible to the eye. Sends pain down arm?

Varies. There are a number of possibilities; from an enlarged lymph node, to a growth of a tumor or an infectious process among other possibilities. If it is red, painful, enlarging you should probably be seen immediately. If it is not, you could potentially moniter it and if it does not resolve over 4 weeks be seen. It is hard to say more without a direct examination. .