A couple of things... I'm not sure what you mean by "spewing slime"... but if you meant a green tinged foam at the mouth, that could be just food tinted foam from a horse that's "mouthy" as we term it here in the western U.S. with our cow ponies. Excess salivation due to working th emouth... usually some kind of mouth tenderness and, since she's a filly she may be teething.
Secondly... has she been near a group or even one or two other horses? Horses catch "cold" from other horses and can spread through a small heard very quickly. It's not actually a human "cold" of course, but it is a virus caused ailment very similar. It usually lasts only a very short time... maybe two or three days and will cause some nose drainage (green usually) along with excess saliva that can be greenish tinted. Horse will usually be somewhat lethargic and off feed. Eyes are usually dull.
Check for any hot spots on your filly... especially the frog of the foot, for noticeable increase in temperature. Barring that, just keep an eye on her, as I'm sure you're already doing.
Any recent change in diet?