Might be a good idea - but when you added a second account, did you disable sync on the first account? If it is account specific, as long as sync is enabled, even if you're only in the second account, it will try to check the first account too.
Also, did you check on the computer if, when composing messages, if they're actually being delivered? if they are being delivered, then it's not the sending of messages itself causing the issue, it's the subsequent check for new messages 8after* sending that is causing the issue.
And if that is the case (that this is account specific), I suggest making a new 'folder' in GMail via your PC (GMail calls them labels, but essentially, they act as folders) and then moving everything in your inbox to that folder (temporarily - you'll move it back later). try syncing your phone. if it still happens, manually clean out your spam folder from a PC (link is at the top - empty spam, I think it says) and try again. If it still happens, make a new folder and move all your sent items stuff to a new folder, and then try again.
If after all this it is still doing it, then something gone screwy with your phone - you could try using the FXZ file to restore to stock (just in case it is an app issue as opposed to a connection issue and / or specific account issue) or, you could take it in to VZW and let them fool with it. Your choice.