Could the mobic (meloxicam) I'm taking for my arthritis be causing stomach pain?

Yes. All of the NSAID medications including Mobic (meloxicam) can cause gastric irritation.
Yes. Mobic (meloxicam) is a nonsteroidal anti-inflammatory drug. These drugs can potentially cause gastritis, esophageal reflux disease [heartburn or gerd], and bleeding ulcers. It is important to take these with food and water, and contact your physician if you start to develope stomach pain.