I hope someone can help you. I have never stitched an afghan so I googled it and completely came up empty on this one :( Do you know what type of fabric it is? Maybe I can find something using the name of the fabric.
Crochet or knit? My mom crocheted granny squares for her bigger afghans. Maybe it's the type of yarn you are using. In my learning to crochet I've found yarns that I won't work with again because they get nasty, that's just making a scarf.
I've never stitched on an afghan, but I bought some fabric to try it, so I also want to know the best way.
Are you using a hoop? It sounds like you need to minimize your hand touching the fabric. When I stitch on regular fabric I use a scroll frame or q-snaps on a stand, with one hand above and one below, so I don't touch the fabric as much. Also, try starting at the upper left (if you're right handed), and move down and to the right, again to minimize contact.