Yes, in general, it is a violation of federal law to "tamper with" or prevent delivery of the US Mail. However, once it is "delivered" to the proper address, it raises the question of whether the feds have jurisdiction over who in your household has the express or implied right to receive, handle or open your mail. For instance, they could bundle up your mail and send it to you via any means of carriage, if you're away, or simply hold it for you until you return.
Because you're over 18, your crazy mom may be considered a "trustee" in possession of your mail and you could, in theory, enforce your right to possession and privacy of your own mail. You can also get your own post-office box and have your personal mail sent there instead of your home.
There is a law against opening mail that isn't yours but I don't think there is a law against throwing away someone's mail. Here's a great link for your for more info.
Call your doctor's office to verify your appointment info. As for your job info, are you allowed in the house? Does your keys still work? You may want to check your home, she may not have thrown it away. Be safe and wish you the best of luck. Don't break any laws trying to retrieve your stuff.