Okay, it is very common in the upper arm to have fatty tumors or otherwise known as lipomas. They are benign, and cause you no harm. However, they can grow near or close by other structures and then cause pain. The location you are describing has many nerves, and those nerves feed your whole arm.
So, a 1 inch lipoma is irritating a nerve in your arm, and that is the radiation that you are feeling. One issue to make certain of: are we certain this is a lipoma? Usually by exam and location, we can diagnose a lipoma. The area you are describing does not have lymph nodes or other possible structures that it could be. But if you have pain, this is an indication well recognized to remove it, if you so wish. The signs that this is NOT a lipoma are rapid growth, irregular shape, unable to move it at all, very hard consistency, and lack of pain. Yours sounds okay. But always, we have to say, to be absolutely certain, it needs a biopsy.
If it causes you pain and we are not 100% certain it is a lipoma (we never can be), then biopsy by way of removing it completely often is the thing to do. Most general surgeons or orthopedic doctors can do this, but you need a referral from your doc.
That's the whole story. Ibuprofen may bring relief as well as icing it down. But it sounds like it bothers you enough to just get rid of it. Depending on how deep it is, doctors can even do it right there in the office.
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Ask any questions you need, I am happy to help.
Best of luck and Godspeed--