baby throws up food

I exclusively BF and pump while at work.. my Lo just turned 5 months old 4 days ago.. she’s eating 4oz every 2 hours when I pump.. she’s getting enough milk but is 10lbs 12oz.. she was referred to a pediatric GI specialist bc they are concerned about her weight. lactation consultant told me it could be due to her throwing up majority of her food half of the time.. she holds it down sometimes and sometimes she doesn’t.. it’s not spit up it’s throwing up and i’m so irritated at this point. she said she wouldn’t consider her failure to thrive because she’s very active and said she has seen some babies that had failure to thrive and be completely drained and not even playing etc. so that makes me happy but i’m currently trying to get her to gain weight.. they want me to supplement for now but I simply just don’t think I have to because she’s getting enough I think it all depends on her keeping down her food.. it’s pretty frustrating at this point she’s so tiny for 5 months☹️