Does a graphic/visual designer who doesn't code technically fall under the UI or UX design category?

UI Design is also known as interaction design. You are designing user interfaces and how people interact with them.  Doesn't sound like you are doing that. UX Design is the holistic design of the experience. From training to product to support and renewal, its global. UX includes information architecture, graphic design, work flow, etc etc.  Doesn't sound like you are doing this either. Graphic or Visual design is when you are using photoshop or illustrator or similar to define the look and feel. Colors, borders, shadows, gradients and other visual treatments are all graphic design. Based on your question, sounds like you are a Graphic Designer. Does this help?

If you're not talking to end users you would be doing UI design. Someone else (UX designer) would gather user needs, work flows, user test results and give you input to mockup screens, which you hand off to the UI Developer to code.

User Experience design is a field of practice. User research, information architecture, interaction design, visual design and motion design are disciplines (specializations) within the field of UX design. Some designers are generalists, doing all of the above. Don't let that throw you. The most successful designers and organizations understand the value of specializations in the field. Visual designers design interfaces. Interaction designers design interfaces.  Graphic designers design print pages and one-off layouts. Graphic designers don't design interactions or interfaces.

you're a UX Designer. As I face such coincidences if I said am a UI designer they think am into HTML and CSS thingies. While the final thing I deliver is the visual design on psd or ai files.