Water heater sound like filling up

[Kitt09]

My water heater has sounded like it's been filling up all day. I can hear water activity, and I think the water tank is filling up. There is no dripping and no water on the floor. I'm working from home, and I can hear it frequently and haven't heard this before.
Is this something I should be checked out? Is it possible it's leaking to an underground pipe that's being metered, and I'm going to get a more massive bill?
My neighbor, who had a similar problem, suggested a plumbing service and told me that I should contact them. Is there anything I can do before contacting them?

[joed]

Do you have a water meter? If so check it and see if it is spinning.
Water heaters sometimes do make noise when heating.