Many knitters slip the first stitch to keep the edges smoother, if you're increasing at the start of a row, it may be best not to slip the first stitch, but to do the increase with that first stitch.
Here's a whole list (as on wiki but with videos) of different increases: http://www.knittinghelp.com/videos/increases
. Best one for increasing by one at the start of a row would probably be what you're doing, knit front and back of first stitch, then continue, no need to slip the first stitch. After you do this just look at your knitting to make sure that your increase looks smooth on the RS where you did the knit increase, sometimes if you don't put the needle in the right way you could end up with what looks like a purl on the RS of your fabric. I can't figure how your horizontal line is forming, but you might be pulling your knitting too tight and it makes your whole row tighten. Is that it?
Does it actually say to do an increase at the start and end of each row or just to increase on both sides? Most of the time increases are done inside the selvedge stitches (like 1 or 2 knit stitches that border your knitting so you can sew pieces together) if doing increases on both side. If it's an increase at the very edge of you rows, then I haven't really seen them done at the start of a row, but rather you do them at the end of each row that you knit, and if you're doing an even number of rows, the increases work out pretty even on both sides.