Can thoracic outlet syndrome cause armpit swelling and dull radiating pain in arm and outer aspect of breast?

May feel like it: If a vascular form affecting venous return, the arm can swell, turn dusky, and ache. The neurogenic form does cause radiating pain and worsens when arm elevated. Aching is often experienced over shoulder blade. Pain over lateral chest wall may indicate the "pectoralis minor" variant.

Perhaps: Venous congestion and thrombosis can occur and make the arm and arm pit puffy and the nerves unhappy.