While you can use a text box to add a word or two to your Word document pictures, it is easier to position text typed directly onto the picture itself. While Word does not let you type directly onto a pasted picture, it does let you add text to AutoShapes. By turning your picture into an AutoShape, you can type directly on it.
When you find that your header is almost overlapping the first line of text in your Word document, you do not need to make your header smaller; you need to increase the distance of the header text from the rest of the content on the page.