My 8 Year Old Lab Mix, Whom I Have Never

My 8 year old lab mix, whom I have never seen I'll or ever refused food, has not eaten for over 24 hrs now. SHe has thrown up yellow bile, the last time being about 12 hours ago. SHe does drink water and her stool had tons of twigs and entires leaves, which I assumed was the cause of the upset stomach.

Her nose is wet, she doesn't feel abnormally warm, n does other routine household actions such as bark at outside sounds etc.
HOWEVER:
She acts very tired-- sleeping a lot ( no energy as hasn't eaten or is it more?) plus I'm concerned at HOW LONG is ok to go without eating?
Thank you for helping!