Helping people with computers... one answer at a time.
There are things to enable ahead of time if you would like to save your email history, but if they are not enabled then your emails are gone for good.
Is there a way to retrieve my email history after I've deleted them?
Chances are by the time you have to ask, probably not. There are several settings in various email programs that can help, but you do have to set them up before you process your email in order to get their benefit.
Let's review a couple of the common ones. Perhaps they're already set, and you can retrieve what you're looking for.
First, many programs have recycle bins. Much like Windows, if you delete an email, it gets placed in the Recycle Bin instead of "really" being deleted. The Recycle Bin gets emptied either when you explicitly do it, or if the option is set automatically when you exit your email program. Have a look in your Recycle Bin if you have one.
Some email programs can be configured to automatically save sent messages. Outlook, for example, has a separate "Sent Mail" folder that keeps a copy of every message you send - if you've turned it on. Many email programs have similar settings.
Email programs that support "rules" or actions that can be taken when email arrives can be configured to save a copy of incoming email as well.
Finally, another option particularly useful if you're traveling is the option to "leave messages on server". Normally when you download your email, it's removed from the server that was holding it. As it implies, you can instruct many email programs to leave the messages on the server, often specifying an optional length of time before they're automatically deleted. If the messages have been left on the server, you can typically use a different email program, or webmail access, to view the messages again.
The bad news is that most of these items are optional and most default to being turned off. So if you haven't turned them on, your delete may in fact have permanently deleted the message.