Welcome to KH!
Since it's double moss, you would start and end row 2 with a k1. Because you've added a stitch at each end, the row becomes:
p1, k1 to end ending on a k1
Every time you increase at the ends the pattern expands a stitch at each end.
For me, the easiest way to do this is to look at the stitches on the needle. You know that you want to maintain that pattern, so just look at the second stitch on the needle and use that to tell you what stitch one should be. If stitch 2 is going to be a purl, then stitch 1 should be knit; if stitch 2 is going to be knit then purl stitch 1.
may help to visualize the increase. The example uses an edge stitch which you may or may not want to use.
Good luck with your sweater. Sounds like you're coming close to the end. We'd love to see a picture if you'd like to post one.