How to apply my deep learning model to a new dataset?
There is a difference between using pre trained weights and transfer learning.


When you use pre trained weights and re train all the layers in the entire model for the dataset, then you are just working towards converging faster in the direction of better results.
If you were to only train the upper layers and lock all the other layers from training, then you are implementing transfer learning.


For your problem at hand, I would use approach 1. 

Would be more than happy to elaborate in case you want me to.

Here is a link that explains how to do transfer learning with Keras : https://towardsdatascience.com/transfer-learning-using-keras-d804b2e04ef8