I'm sorry to hear that that is your outlook, however to use your own point against you; you are
only 18. I know the world expects you to be a proper adult and have everything sorted out by now but that isn't the reality for a very large number of people. At 18 you still have about 50 years of working life in front of you, so there is every motivation for you to turn things around. Any ages by which you're 'supposed' to have reached certain milestones are completely arbitrary and don't take into account people's personal circumstances; you mention that you have health problems so it's perfectly reasonable that things may take a little longer for you, and that's okay. Hey, sometimes I feel like a failure because I'm 21 and I can't drive yet, but I'm sure you'd agree that that's a ridiculous mindset! The same goes for you; the age by which you reach certain points does not define you! One of my friends had to sit GCSE maths 13 times before she passed, but she got there eventually and none of her employers have ever asked or cared if it was from her first attempt.
Have you been receiving medical attention for this? I absolutely sympathise with your health problems and I fully appreciate that none of these conditions are something that can be alleviated with a magic pill, however I would really recommend speaking to someone about how much impact this is having over your life. Working as a vet care assistant is liable to be a stressful job that requires you to be on your feet a lot, so the first priority would be to ensure that this doesn't make your current conditions any worse.
From what I've seen, most jobs with animals care a whole lot more about your prior experience than your GCSEs. After all, it's more important to them that you aren't scared of dogs and don't mind cleaning up cat sick than whether or not you can explain the formation of an ox-bow lake or write about what you like to do at the weekend in French. Voluntary work is therefore an excellent in road; and myself and a few people I know have been offered jobs at farms, kennels and veterinary practices after spending some time doing unpaid work experience.
If you are still finding that your lack of GCSEs is restrictive, then could I suggest retaking some subjects (specifically maths and English as these are most important and because you will probably find these reasonably straightforward after completing your functional skills qualifications). You could potentially do this while still working, for example through distance learning or evening classes.
Best of luck for whatever you choose to do