This paper proposes a novel adaptive tracking control approach of state-constrained nonlinear high-order systems (NHOSs). By introducing a coordinate transformation function that depends only on the state of the system, the asymmetric time-varying state constraints are addressed directly. Compared to the existing schemes, the constraints imposed by the reliance of virtual control functions on the feasibility condition (FC), as well as the dependency of tracking performance on constraint functions, are both eliminated. At the same time, the requirement for constraint functions to be bounded is also removed, which ensures that the proposed method remains applicable to unconstrained NHOSs. Moreover, by utilizing fixed-time stability theory (FTST) and event-triggered control (ETC) incorporating an enhanced adaptive event-triggering mechanism (ETM), the closed-loop system achieves fixed-time stability while significantly alleviating the communication load. The effectiveness of the proposed approach is confirmed through simulation studies.