What you need to do is check what the position of your picture is. Word uses an "Anchor" to determine what the location of the picture is attached to. If the picture is anchored to a particular page, then the text can move or float around it. If the anchor is connected to a particular paragraph, then the picture will move together with the text if new text is inserted above that paragraph - but not if the new text is within that paragraph, between the anchor location and the picture position.
Whether anchors are displayed or not is an option. Go to Word Options --> Display --> Always show these formatiing marks on the screen --> Object anchors - and put a checkmark next to that line to always see the anchor.
Alternately, go to the Home tab, in the Paragraph group there is a latin Pie symbol (¶). Once you do that you will see all the formating marks, including the anchor for the picture, once you click on it.
First drag the picture to reposition it relative to the text to where you want to leave it, then drag the anchor to a spot in the text where you wish to anchor it. The beginning of the preceding paragraph may be a good spot.