Just from personal experience, after a month 3 miles should be feeling a lot easier unless those hills are pretty stout.

I can't stress enough the importance of getting your seat at the right height (probably up). If it's an inch two low, even an easy climb will start burning your legs something fierce. I can definitely tell when my seat's slipped down, my legs know it as soon as I hit the hills.

Gearing too, as mentioned. I'm pretty sure every newbie, myself included, uses too high a gear. For me, I felt good if I could get going fast in the highest gear, which is silly. Now I spin a lot faster, my legs don't hurt, and I go a lot faster. Oddly enough, I've found for a while now that the stronger I get as a rider, the less I use the highest gears.

Maybe get a cyclocomputer (speedometer) to see how you're doing. As with the LeMond quote, you might just be going faster now! If you see the improvement, you might not mind the pain.