What's the difference in height from the top of your saddle to your handlebars? How tall are you? You say the "bike seems to fit well" but you are getting neck pain - what does that mean?

I used to get neck pain and switched from a 120mm to a 110mm stem and flipped it so it was angle upwards. That helped a lot.

If your stem is currently flipped downwards, then maybe you could just try riding with it angled upwards and see how you go? There is no harm in trying it out to see if it helps, it only takes 10 minutes to flip it.

You really shouldn't have to be taking pain killers after a 30-mile ride!!