I'm not sure I understand the question. Are you asking whether we say "I'm going to hospital?" as opposed to "I'm going to the hospital?"
Yes, we do. Like "I'm going to school" or "I'm going to jail", the definite article is not spoken when referring to it as a general state. When referring to the actual specific location, though, we say "the prison" and "the school" and "the hospital". "I applied for a cleaning job at the hospital" is correct, as is "he has been contracted to do some repairs to the prison roof".
You do the same thing as us with school, college, jail, and other words. You have a special exception for hospital, though. We don't.
We don't say "I'm going to doctor" though.