Count the stitiches on your needle, are there more than when you started? You may not be completing the knit stitich when you pull it off the needle.....which results in a yarn over effect and increases the number of stitiches. Sometimes that happens when you are new or in a hurry.
The other reason, if the number of stitiches is the same, is that as a new knitter your stitch tension is not consistent (some more loose than others) which can make the width variable.
A scarf is a great first project, by the end of it you should have it down pat!!!