Note: For ease of explanation, I will use one of the analogies from my comments (window cleaner with fear of heights) a number of times in the answer.
Your issue here is one among a class of issues wherein a job involves doing a certain task repeatedly, but the task or a certain portion of it triggers some kind of fear.
Just to give you a "you are not alone" feel, other examples of such pairs of professions and fear would be: 1. window cleaner/fear of heights 2. firefighter/fear of large fires 3. lifeguard or swimming instructor/fear of water bodies 4. politician/fear of public speaking.
I will not offer you a "do this" solution, but provide you with options. Which one you choose depends on your life priorities, so you have to make that decision for yourself.
Option 1: Get another job which does not require regular (or any) high speed driving.
A person with fear of heights will be unable to work as a window cleaner (which would often involve cleaning the exteriors of tall buildings). Finding a job which does not involve such heights is a reasonable option.
Option 2: Work on eliminating the fear
If you absolutely must do this job (for whatever reason that is important to you), you need to work on how you could eliminate that fear. Seeking medical help is a good starting point, but I am not a medical professional, so I won't go offering pseudo-expert medical advice, which will only cause harm.
Option 3: Negotiate other work options with your manager
If you take Option 2, you would most likely also need to do this in the interim until you succeed in overcoming the fear. However, you could also do this instead of Option 2.
Ask for a 1:1 meeting with your manager, express your concern, and ask if you could be reassigned to another role which requires less or no driving. The support you receive and the outcome will vary based on the company's policy and the company's size, and perhaps also, based on other factors such as your rapport with the manager and his personality.
Going back to the analogy, our window cleaner friend may get responses ranging from, "I am afraid if I cannot expect you to clean the exterior of a window on the 200th floor, you would need to seek other employment options" to "Okay, I understand, let me move you to the floor cleaning department, where you won't have to deal with heights."
Note though that, if you negotiate a "limited driving" role in your current role (as against a completely different role), you put the company at some disadvantage. Depending on company policies and local laws on discrimination (fear of something could be considered a "psychological disability" with sufficient lawyering), they may renegotiate your salary or other benefits.
So, to summarize, what you should do depends on how important this job is to you, how easy or hard it would be to find other kinds of jobs, how much effort you are willing to put to lose the fear.