I failed a written exam and I don't know how to reply to my professor As a preface, I would like to explain that  have ADHD and anxiety issues and tend to be very slow at writing (mostly due to overthinking/over-analyzing and having OCD-like tendencies when writing).  I also made the dumb decision of not going into academic services to ask for accommodations (partly due to anxiety).

Due to the stay at home order the exam for my class was changed to have only written response questions (thankfully the professor changed it to open book). We had the whole day to work on it but then it was time to turn it in, I had only a third of the questions answered.  Yesterday  I received an email asking about why the exam was sent incomplete  and if I sent the wrong one. I had a minor anxiety attack and made a  unwise decision of avoidance. Today, I am trying to write a reply to my professor's inquiry and have no idea how to explain it. I'm worried that my professor will think that I don't care about the class and that I'm slacking off.
Tell the professor what happened.  If the professor already knows about your issues, there's no need to belabor them further.  If not, summarize as you did in your question here.

Explain that it was incomplete because, although you worked for the entire allotted time (if you did), you didn't finish.

Your question suggests that you may be used to an oral component on exams.  If that's the case, perhaps the professor would examine you by telephone, or Skype, or something.

The professor's email, as summarized by you, shows that the professor cares about you and wants you to do well.

Addendum: If you have academic trouble, always start with the professor.  If you get an answer you don't like, you can then move on to department heads, academic or disability services, etc.  Please give the professor a chance first.