Earlier today I stupidly applied glitter polish on my toenails right before I started my yoga class and apparently one of my nails hadn't fully dried yet and stained the back of my new workout leggings! I came here to try and find a solution and unfortunately we don't have any oven cleaner or acetone-free nail polish remover in the house at the moment, so my husband made a mixture of dishwashing liquid and white vinegar and applied it with a cotton bud to the stain. After a couple of minutes of gentle rubbing I rinsed it and it had lessened significantly! He continued applying and after the second rinsing there's almost nothing left. A few of the glitter grains even came off while I was rinsing. Hope it works for you!
Depending on the fiber content of your sweater there are differing methods for removing a nail polish stain. This is a page about removing nail polish from a sweater.