Catheters assemblies having structural configurations operable to reduce backflow along the catheter assembly track, and methods of making and using such catheter assemblies. Catheters assemblies in accordance with embodiments of the present invention find use in various applications including the treatment of acute and chronic medical conditions. An exemplary catheter assembly includes, in one illustrative embodiment, a flexible proximal catheter body portion, and a distal portion of a smaller diameter than the body portion. The distal portion includes a sealed distal tip or end and one or more side flow openings to permit flow of therapeutic substance from the catheter along an axis that is different than, e.g., skewed relative to, a longitudinal axis of the distal portion of the catheter assembly.