Maybe you need to give the text in your header a 100% size, rather than a 38px size.
If you're not using a Child Theme, and if the theme doesn't have a designated section of the dashboard for CSS modifications then install this Custom CSS Manager plugin http://wordpress.org/plugins/custom-css-manager-plugin
Then use its "CSS Code" section of the dashboard to hold your CSS modifications:
Alternatively use your Child Theme style.css file to hold your CSS modifications:
@media screen and (max-width: 320px) {
#logo {
font-size: 100%;
}
}