No heat, until driving it for 3 miles

Ok, So, first, if this answer to my question is really easy, forgive
me.

About 3 weeks ago, I noticed that when I turned on my heat, it
wouldn’t come. So, I checked my coolant (yes, I can do that) and it
was bone-dry. So, I filled it. And, it kind’ve worked again,
however, it didn’t kick in until I had been driving the car for about
3 miles. Then that night, I got back into my car after work, and no
heat again. When I got home, I checked, and again, my coolant was
dry. So, I filled that up again, and looked under my car, and I saw
an almost steady stream of the yummy antifreeze creating a puddle
under my car. I’ve been checking everyday since then, and usually, I
would have to fill it every 2 days, or so. However, this is day 4 of
me not filling it, and it’s still full, I think it has a mind of its
own. I bought a new water pump, as my mechanic said "it could be
that," as he looked under my hood, and saw steam coming from where he
said it was located. I haven’t had the chance to get that done yet
though. So, my car, while warming it up, isn’t getting the heat I
want it to, and doesn’t usually warm up for a couple of miles. Can
anyone tell me if it does sound like a water pump problem??? Or does
it sound like something else?

 

first things first - identify the source of the leak. proper
inspection. after that, and when you're not losing coolant, /then/
worry about the heat. chances are, the problem will have gone away.