How will having broken collar bone affect my long-term health?

It depends: Most likely no. You may have a lump over the fracture result from healing; some people do not like this from cosmetics point of view.

Should not: Majority of clavicle fractures heal uneventfully unless severely fragmented, shortened or located more at distal end of bone (closer to shoulder). Once healed there will likely be a prominence at the sight of healing but should not be painful. Persistent pain for more than 4-6 mos suggests failure of healing and surgery could be necessary to induce healing.