Upper arm stiffness and pain in both arms can't carry my baby?

Hmmm? When both arms are involved i think of either something in your neck like a pinched nerve or simply overuse from lifting too much. Best to get some help with the baby and see if things settle down.... If not get it checked.

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What could be a major arm pain in both arms?

Cervical disc. A central bulging disc can put pressure on the nerve to both arms giving you your findings. You need to see a spine surgeon. Read more...