Megan - Yes, clear out all messages as you read them until you are added to your new House. Until that time, I believe you are only allotted three spots in your inbox. If we (mods) are unable to send you your results from the Sorting Quiz due to a full inbox we will usually alert the others mods who come in to sort people and ask that they try resending it the next time someone logs in to the Sorting Hat account.
I hope that makes sense.
Regarding the error messages, some people swear that if they log off/delete their cookies, it fixes things. You might try that, otherwise I'm not going to be able to help you.