Cold + Vomiting?

So it seems like my babe has struggled to breathe through her nose for the last few days and has been coughing on an off. Just a bit ago, she woke up sort of and choked a little bit like she wasn’t breathing right. Then I pulled her up because she was coughing a bit more. She proceeded to vomit or at least attempted to...

She did it again about 10 mins later after crying, and that time some mucus/spit came up. She fell back asleep on her baba after calming down... should I attempt to feed her when she gets up?

Is this normal? This is probably sounding crazy paranoid...I have an extreme aversion to vomit.. ( ridiculous I know)