Yes, I do think you are worrying too much. As you and your husband get older, you have more responsibilities and less time for emailing and chatting. That happens to just about everyone. It is very unusual for partners to be in touch 5 or more times a day.
Both of you need to be free to focus on your studies or work. With so many years of history, you and your husband should be able to relax in each others’ love and support and not need constant reassurance. That is what it means to trust.
I understand that you and your husband are trying to maintain connection despite living separately. I suggest that the two of you agree to a “check in” time each day to chat with each other and share what is going on in your lives. Let’s say the two of you decide that from 5:00 – 5:30 each afternoon is “couple time.” Having the certainty of a time when you will talk or Skype would let you focus on your studies during the day. If you think of things you want to share while you are studying, write them down and save them for your check in time.
Your husband will be home in a few months. I imagine you both want to have a strong academic and occupational foundation for your life together. You will bring more to your marriage if you pass your exams. If you think about your studies as a contribution to your marriage, you may be able to focus.
I wish you well.