Does traumeel contain white willow bark in it or anything else someone allergic to aspirin should not take?

No problem: Willow bark contains salicylate which is well tolerated by people having adverse side effects from aspirin. Aspirin is acetylsalicylate which is different from salicylate in pharmacologic actions.

Traumeel: See: Traumeel – an emerging option to nonsteroidal anti-inflammatory drugs in the management of acute musculoskeletal injuries at https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3085232/. I just checked a tube of Traumeel and did not see white willow bark listed.