I think you don't need to Learn Programming Language like C,C++ or VB.net .. it's easier for you to learn MATLAB , because it's Mainly designed for people like you ( non programmers)
and maybe you can see some videos in youtube about something Called (Weka) .. it's analysis tool, it will allow you to do very great gob with data analysis .
Any medical personnel these days must be computer-literate or -savvy. You need to know the basic concepts behind computation. You must know the meaning/ definition of computer-related terms like input, output, algorithm, program, code, hash, etc. I would advise reading an entire dictionary of computer terminology. Proficiency in at least one computer language, e.g., Perl, python, etc., would help a lot in your understanding of computer terminology. It will also prepare you for personalized medicine a.k.a. precision medicine, that is looming on the horizon.
A lot of medicine equipment could provide data in DICOM format (Digital Imaging and Communications in Medicine). So it's very useful to know some image processing tecnique and some programming skills. As mentioned Matlab, may be IDL or Python. Anyway, the programming knowledge will help you to set more specific task for programmers.
Python will be best for you. I recommend you read this document to see what you can do with it. I worked 7 years in the development of educational medical software and I learned a lot about medical terminology and even interpreting electrocardiogram (ECG) charts. Have that knowledge made it easy for me to design and implement the software.
My advice is "Yes". Even engineers are learning about biological behavior of humans to build systems. I can tell you how programming will helpful to you and some recommended programming languages.
When you will be a doctor, you might come up with hundreds or may be thousands of patients. With your experience you will realize that there is a some kind of pattern of patients related with particular symptoms. You wanted to know how this symptoms related to particular cause. Since you do have lot of data it is not practical to analyze those data on your own. Instead of that you can use those digitized data with machine learning to predict or to identify the correlation of the symptoms with the patient's state. This machine learning thing will work based on probabilities, statistics etc.
You might get afraid with the the big buzz word "Machine Learning". Fortunately developers have done the tough part for you. In python you only need to write few lines of code and there are more tutorial out there in the internet to learn these stuff. You just need to understand the basic how things will work.
So I suggest you to learn python. It is a programming language which is easy to learn and can apply in many scientific areas. :)
I think it worth leaning one or two programming languages, eg, Python, R etc. In particular, medicine students want to do research on biomedical informatics or biomedical engineering in the future.