Currently available risk prediction methods are limited in their ability to deal with complex, heterogeneous, and longitudinal data such as that available in primary care records, or in their ability to deal with multiple competing risks. This paper develops a novel deep learning approach that is able to successfully address current limitations of standard statistical approaches such as landmarking and joint modeling. Our approach, which we call Dynamic-DeepHit, flexibly incorporates the available longitudinal data comprising various repeated measurements (rather than only the last available measurements) in order to issue dynamically updated survival predictions for one or multiple competing risk(s). Dynamic-DeepHit learns the time-to-event distributions without the need to make any assumptions about the underlying stochastic models for the longitudinal and the time-to-event processes. Thus, unlike existing works in statistics, our method is able to learn data-driven associations between the longitudinal data and the various associated risks without underlying model specifications. We demonstrate the power of our approach by applying it to a real-world longitudinal dataset from the U.K. Cystic Fibrosis Registry, which includes a heterogeneous cohort of 5883 adult patients with annual follow-ups between 2009 to 2015. The results show that Dynamic-DeepHit provides a drastic improvement in discriminating individual risks of different forms of failures due to cystic fibrosis. Furthermore, our analysis utilizes post-processing statistics that provide clinical insight by measuring the influence of each covariate on risk predictions and the temporal importance of longitudinal measurements, thereby enabling us to identify covariates that are influential for different competing risks.