Pointer analysis is foundational for many static analysis tasks, yet its effectiveness is often hindered by imprecise modeling of heap allocations, particularly in C/C++ programs where custom allocation functions (CAFs) are pervasive. Existing approaches largely overlook these custom allocators, leading to coarse aliasing and low analysis precision. In this paper, we present CAFD, a novel and lightweight technique that enhances pointer analysis by automatically detecting side-effect-free custom allocation functions. CAFD employs a hybrid approach: it uses value-flow analysis to detect straightforward wrappers and leverages Large Language Models (LLMs) to reason about more complex allocation patterns with side effects, ensuring that only side-effect-free functions are modeled as allocators. This targeted enhancement enables precise modeling of heap objects at each call site, achieving context-sensitivity-like benefits without significant overhead. We evaluated CAFD on 17 real-world C projects, identifying over 700 CAFs. Integrating CAFD into a baseline pointer analysis yields a 38x increase in modeled heap objects and a 41.5% reduction in alias set sizes, with only 1.4x runtime overhead. Furthermore, the LLM-enhanced pointer analysis improves indirect call resolution and discovers 29 previously undetected memory bugs, including 6 from real-world industrial applications. These results demonstrate that precise modeling of CAFs has the capability to offer a scalable and practical path to improve pointer analysis in large software systems.