As I understand it the wallet is stored on the browser moved to other comps and browsers via the bin. file
Yes (afaik internet explorer is not supported)
Can I move the offending account to my current wallet without the bin. ?
bin is your wallet it is tied to the account name, however inside that account you can create another wallet and account, which is not very intuitive to manage.
Would be much easier to help you if you describe step by step how you created those 2 accounts.
Like:
I came to openledger, used this machine, that browser, created account, made backup (backup_name) and so on...
Its hard to guess what you did, because there is many options. If u are sure that you have all backups, dont panic, you're safe.