Yes , it is very possible to have bilateral tos.

Have you had X rays or MRI to check for extra cervical ribs?
And any other bone anomalies?

VTOS (vascular tos) does have hte bes surgical outcome.
With an expert TOS surgeon ( the only ones I would consider for any TOS surgery)

Look up athletes that had TOS, of course often it doesn't say if NTOS or VTOS in those articles.
But when a nerve is involved it is a very different animal..

Use our search tool to look for other vascular & clot postings.

At your young age and wanting to be active again, I would seek TOS pros for evaluation/assessment , and not waste time with any MDS or PTs that are less knowledgeable.
If no one sent you for any imaging ye to check for actual causes, they are lacking in TOS knowledge.
You certainly don't want to be on thinners forever..
http://neurotalk.psychcentral.com/thread135.html
http://neurotalk.psychcentral.com/thread84.html