Bed bugs and carpet beetles
what do you recommend for a chemically sensitive person to treat for bed bugs AND carpet beetles? do you agree that the picture is of bed bug and carpet beetles?
Your photo is not clear enough to tell for sure if you have a bed bug there. If you can send a better photo that includes the head, that would help. You could attach it right to this reply.
It does look like possible carpet beetles though.
You don't need any pesticides for them, as sanitation, primarily through vaccuuming is most important. Pay special attention to often undisturbed areas, under and behind heavy furniture and along the wall crevices, using a vac with a hose.
This page has more: https://extension.umd.edu/hgic/carpet-beetles
For most insects, non-chemical controls include getting rid of clutter, regular vaccuming, proper storage of cleaned woolens/furs and laundering of fabrics, including heated drying is helpful.