I'm glad you are ok.
You're right, keeping on trying is what leads to success.
Nothing good comes easy.
I don't think you should be grateful for what job you get.
If you don't want to do care work then I think you should avoid it as far as you can without getting sanctioned.
Believe it or not you are in a good position because at least you know the sort of work you would like to do. Many people don't have a clue.
I hope you continue to stand up for yourself and work towards the type of job you want. I know it's tough without experience.
I know five ways people have succeeded.
Some have gotten the qualifications.
Some have done lots of volunteering in the area they want to work in to gain experience.
Some have just gotten lucky.
Some have gotten a really poorly paid job to start with,
a friend got his start in IT by being a 'tech' at pc world. A few months of that along with some night school was enough to get a job in an IT support role.
After that he got better and better jobs till he got one he wanted.
The most successful people seem to have mixed all of the above, volunteering while getting qualified then taking a really low paid job in the area they want to be in and working up from there. Luck always helps too
If you keep trying, I'm sure you will get there.