There are people that have had the accounts un-flagged. But usually it was cut-n-dry... The person only ever had one account, and the person didn't cheat, etc. And, in those cases, the accounts were restored and the prizes shipped ASAP (or tickets refunded if the prize was no longer available). However, most people get the cold shoulder once they have been flagged and it is common for them not to get any response to their inquires once they get their 'you were flagged' email.
Bing can lookup all past orders, and they do so when checking to make sure you haven't previously ordered the same prize (i.e. limited to 1 of each prize per address) as well as to check if you are trying to use multiple accounts to avoid the daily ticket limit (i.e. violating the ToS).
My guess is that they the flagged both accounts for violating the multiple account rule. And, I suspect that they aren't going to care much about your sob story. With the number of people that have been abusing the site, and that are now trying to find ways around the recent rule enforcement changes, I would guess that they have heard it all already, many times.
So, I would suggest that you 'retire' those accounts. Just let them go. They are flagged, and the chances that Bing would unflag them is slim to none.
Wait a few days, and start new accounts. Then, just in case, I would strongly suggest that you use a different name on your orders (variation on your first name, nick name, first in initial only, etc) and only use the email address you used to create that new account.
Just keep in mind that any prizes you ordered on those accounts, even if you didn't receive them, still count towards the 1-per-address limit, so you won't be able to re-order any of those specific prizes.