the "x" in cornish X is a shortened way to say cross. So yes, what you have is a cornish cross. While you can try your best to give this chicken a good life, I've never seen a cornish X (cornish cross) live for very long at all.
Hey Im really worried for this chicken. You should try feeding it something nutritious like a hard boiled egg until the chicken food gets there. My birds go crazy for them.