It is not that bad

Take it easy, it may not be that bad. If it is for full time employee position, people will not reject you just because of that. Contract job depends though.

Who did you send the eamil to? HR people does not have authority to approve the leave, it up to the manager. As manager, he may not have time to answer you so soon. Manager have a lot of things to do, your request probably at the bottom of his to do list.