These are multiple non-fatal events per person, so it seems that with few if any exceptions there will be right censoring after the last recorded event.* After the last recorded event there is at most a lower limit to the time to the next event. That type of censoring isn't necessarily a problem per se, as survival analysis is designed to handle such right-censored survival times.
There can be problems if censoring is informative. To evaluate that, you need to apply your knowledge of the subject matter to your data collection and modeling strategies. See this answer for an introduction, and this answer for a more technical description. This review provides several examples of how and when censoring patterns can lead to problems. If events are truly independent within an individual, then the distributions of event times and censoring times (each expressed relative to the preceding event) should provide no information about each other, consistent with non-informative censoring.
I'm actually more worried about your assumption of independence of events within individuals, as that's a pretty strong requirement. You might want to consider more flexible ways of evaluating your data, for example with plots of cumulated hazard over time (at least to help evaluate the assumption of independence), models in which the number of prior events affects the hazard of a subsequent event, or multi-site models. The vignettes for the R survival package provide a good place to start to look for guidance.
*Unless you are also modeling death in a multi-state model there should be censoring at time of death, as that's a competing event that clearly changes the probability of further non-fatal events.