when you say "the first 8 rows are knit" do you mean you've just completed 8 rows, or you have 8 rows of knitting (but no purling)? If you're doing 1 row of knit and 1 row of purl, you'll have curling - that's just the nature of that kind of pattern. (Have you seen hats with curled brims? They do that by knitting a row and purling a row (stockinette stitch).) If you do every row knit, you shouldn't have a curling problem. Even if you knit tightly.
For only 8 rows, I'd be tempted to frog it all out and start over.
Try this pattern. Knit every row for 6 rows.
Row 7: Knit across.
Row 8: Knit 5, purl to last 5 stitches, knit last 5 stitches.
Last 6 rows of blanket: Knit across.
Or, if you don't want to do a border, try a ribbed blanket:
Cast on stitches in an odd multiple of 3 (maybe 3x17 or 3x23 or 3x31 - whatever gives you the width you want).
Row 1: Knit 3, purl 3 (repeat across, ending with a knit 3)
Row 2: Purl 3, knit 3 (repeat across, ending with a purl 3)
Repeat rows 1 and 2 until blanket is the size you want.
Note: with the ribbed blanket, cast on a bit more than you think you'll need, because ribbing is narrower than you expect.