I have a mild case of tos, what problems could arise from sleeping on the side most affected by tos and how long can it take to recover from the crushed nerve bundles?

Sleeping with a wrong posture, i.e. raise your arm up above your head, can exacerbate the neurogenic TOC but it should improve by time when the compression is relieved but it is hard to predict the recovery time. If the pain is persistent or it lasts for weeks, you need to see a physiatrist or physical therapist and sometimes medication(s) may be needed.

Dr Le is correct about arm positioning, but otherwise, no symptom exacerbation should occur due to sleep. Have no clue what you mean by "crushed nerve bundles". Have you seen an expert in TOS, such as a vascular surgeon? Have you had an EMG/ NCS of the brachial plexus, or vascular studies of the region? Are you receiving specific physical therapy?