Demi Lovato to Fro-Yo Shop, 'You Don't Wanna Mess with Me'

Demi Lovato isn't backing down in her diet food war with a frozen yogurt shop -- she's now warning the store about messing with her ... but also walking back her comments a bit, saying she was having a really bad day.

The singer continued going back and forth with The Bigg Chill -- the fro-yo shop she attacked Sunday for its placement of sugar-free items -- by sending a DM to them, complaining about the "GUILT FREE" label on cookies in the store. TBC defended itself saying the pic was old.

Demi swatted back ... insisting they carried another, similar "diet culture" cookie -- and also warned TBC to stop fighting with her, and that they didn't wanna mess with her. She even dropped the ol' ... "customer is always right" on 'em.

However, Demi's apparently seen the some of the backlash against her, because she just went live on IG, and restated her initial complaint -- her visit to TBC seriously triggered her eating disorder issues -- but she hopes she's opened a dialogue with TBC about relabeling some products.

She added that she had a very bad day and weekend afterward, and feels like she needs a mental health day. Demi apologized if it seems like she's a big celeb using her power to take down a small biz.