Hi!
Please take a deep breath. It is most likely just either something scratchy stuck under and eye lid or an eye poke that is just about starting to ulcerate but as there is no sign of bleeding and the ulceration is just setting, things are not on the dramatic side.
Good that you are having her seen promptly so you can step in with antibiotic drops or gel ASAP; since eye medication and treatment are the same for all common pet species, a general vet will do.
Please ask the vet for a rehydrating lubricant if they do not prescribe one themselves (more and more UK vets will actually); this helps to speed up the healing process and adds to the eye comfort. You will have to always wait for at least half an hour after applying the antibiotic eye meds (most likely isathal as you are in the UK) before you can use an artificial tear gel or lubricant to allow the antibiotic to be fully absorbed.
If your vet is not prescribing any kind of lubrication in combination with the antibiotic drops/gel, get some from a pharmacy or order online.
Artificial tear gel like viscotears is much easier to apply and longer lasting in effect than drops although drops will do if you cannot get hold of gel; you just have to give them more often, up to 6 times a day instead of just 3 times. My own vet prescribes lubrication now with any antibiotic eye treatment and I have found that it really makes a difference with the healing process. Because I have so many piggies, I always have some gel at home, just in case. It's come in handy over the years!
The eye should look back to normal within a few days but you need to keep applying the meds for as long as you have been prescribed.
The important thing with eye injuries is the prompt action as that means that it cannot deteriorate badly and will heal off again a lot more quickly and easily.
All the best!
PS: My Brathlys has just presented with an ulcerating eye poke last week. Her eye is already starting to look pretty normal again with the ulceration pretty much gone now after three days of treatment thanks to stepping in promptly. The eye should be fully healed off within 7-10 days of the injury happening.