I am not a doctor, but my understanding is that reflux does resolve itself over time. The problem is often that the valve between the esophagus and stomach is underdeveloped, and can't keep the stomach acid out of the esophagus. Once the child matures and that valve has a chance to fully develop, the problem often resolves itself.
In the meantime, though, there is no reason for your child to continue to suffer. If your current doctor refuses to consider treatment, it might be worth trying to get a second opinion. There are several medications that can help considerably with the child's reflux, usually by neutralizing or reducing some of the acid in the stomach. If your current doctor won't prescribe it, you might want to talk to another doctor.
Other things you can do to help
One analogy I found helpful was to think of your child's stomach as a big water-filled sack, with an small, open valve on top. Anything you do to your child that would cause that sack to spill its water will also cause your child's stomach acid to come up into the esophagus. Thus you might want to avoid things like:
- turning the child upside-down (or even prone, in some situations)
- squeezing the child around the middle (or holding them around the middle with their back to you)
- excessive spinning, twirling, jumping, bumping, etc.