It's not that unusual for Personal Assistant roles to include such tasks as making drinks.
Asking while you're on your lunch break is not on in my opinion though - and I would say the same of any request to do a work task while you're obviously on a break.
Fortunately there is a work around for that situation at least - which is to eat lunch elsewhere. Should you have to in an ideal world? No. But this is the world we have and for some reason millions of people out there seem to translate "eating at desk" to mean "yes I'm accepting work requests at the moment".
I made it but was too frustrated to even finish my lunch!
Honestly while I understand and completely sympathize with your frustration I do think this is an over-reaction. If a small, albeit thoughtless action can get you worked up to that extent then you are going to be in for an extremely stressful life in the workplace!
I feel like they don’t see what I’m actually capable of and just see me as the run around. Baring in mind, they have to walk past the kitchen to come into my office to ask me...
I'm not trying to be harsh here.. but "run around" is pretty much the point of a Personal Assistant. It's not that they are incapable of doing the tasks they delegate to you, it's so that they can get on with doing the bits of their job that can't be delegated to an assistant.
Imagine you're the CEO of Acme Mega Corp and one of your execs tells you they haven't finished the Widget report that day because they ran out of time and you've seen them making tea and coffee. You are probably going to be wondering why you go to the expense of employing them a PA.