Anyone else have a teething baby?

Rheanna
My daughter constantly has her hands in her mouth anytime she's awake. I believe she's teething. She's been making herself throw up too and that scares me so much. I will rub her gums and that seems to help for a few minutes then she's got her hands and fingers right back in her mouth. She won't hold a teething ring, I've tried that. Any suggestions? She will be three months next week.