Anxiety is recognised as a disability (mental health conditions count!) and is covered under the Equality Act 2010 (I think that's the right year, I always get confused
). As such, if you have an official diagnosis of anxiety, your university is obliged to level the playing field so that you may reach you full potential, by putting certain things in place.
So for example, you mention lecture theatre environments being daunting. If you have a written confirmed diagnosis of anxiety from a GP or psychiatrist, you can take that to Edinburgh's disability department (even before you start there!) and register with them. They will encourage you to apply for Disabled Students' Allowance (DSA) - I would heartily recommend you comply and fill in the form! If your funding body agree that you have a disability and are eligible for DSA, then they will pay for you to have a 2 hour needs assessment, tailored to your exact needs and problems. They may recommmend a mental health mentor, or a notetaker for lectures, in case you feel too anxious to attend some days (or even every day!). They can provide library support, give you a printer-scanner so that you can do stuff from home, etc. This will all be paid for by your funding body and/or your university.
Even if you decide NOT to apply for DSA (though I really would recommend it!), your university can - once they know you have a registered diagnosis - put things into place without DSA. This could include specifying to lecturers to give you handouts/PowerPoint slides in advance via email, so that if you cannot attend, you haven't missed out. They can specify to the lecturer that you be assigned a seat very close to the exit, in case you need to leave mid-lecture due to anxiety and/or a panic attack. For exams, they can put you in a separate room from everyone else, so that you are not overwhelmed by the number of people.
Literally, there are SO many things they can do to help, and they WILL be happy to help you. All you need is a doctor's note confirming a diagnosis.
Hope that helps a bit