Yes. You do not necessarily need a teacher or a school to train your ears. This is demonstrated by the vast number of musicians who have attained incredible ears over their career, through active and passive ear training, without once being taught it in a classroom.
There are two parts to learning ear training: learning how to do ear training effectively, and actually learning listening skills through ear training.
Remember: Ear training is the process of improving your ears for music. This means that you must learn how to do it, and then use it to learn!
1. Learning how to train your ears
For this part, it is best to find some form of “teacher”. This does not need to be an in-person human instructor, but you want a source of information which can help direct you to the most useful methods, help you find the resources you need and guide you as you plan your training.
This “teacher” could be: