Hello, Connor. You have had lots of useful advice, but I think I can touch on a few points.
First, let us get the statistics in order. Clearly your dad’s needs take up a lot of your time each day. You say you have sent out “thousands of job applications”. Really? I am not being funny but if you have applied for 1 000 jobs in just over a year, that’s about three per day on average. A job post needs to be found, researched and applied for, with all that involves in a covering letter and any application form you may be required to complete. It takes a lot of time. Even with no job or caring duties you would be unable to do justice to job applications if you tried three applications per day. It seems to me as though you are trying too hard, and would be better advised to be more selective in the jobs you apply for and give them more careful consideration.
You say there are always thousands of other candidates. I suspect that that could be another exaggeration. I heard of a case once where a college advertised a post for a caretaker and had well over 100 applications. On the other hand I have known of more than a few cases where there have been insufficient applications to draw up a short list and the post has needed to be re-advertised.
You say you have had multiple interviews. This is what really matters. If a potential employer short-lists you for interview, then it means that they judge from your application that you are well suited for the job. The issue then is that you are in competition with other short-listed candidates, who are also judged to be well suited for the job. Maybe you need to be looking at the way you present yourself at interview.
What type of work have you in mind? You said you did not know even where to start on self-employment. Others have suggested self-employment but if you feel so negative about it then forget it. To set up as self-employed requires much time and possibly money up front. You need to study the market and determine where you will find your customers. You don’t at present have the time or energy to do this. Many self-employed people began by working for someone else and learned the market that way. By all means do a bit of dog walking or window cleaning, if you find such work, to earn a little pocket money. Investigate Substack too. But don’t much time looking around or see this as a way back to a career.
Full-time or part-time? It does not sound as though you can take on full-time work at present. For part-time work you would need to decide how the working day was structured and how to divide the day between working and caring. You need to have this planned, so that if asked in an interview how you would share your life you could give a firm answer that would satisfy the employer’s needs ─ otherwise you will be unlikely to be selected.
I presume that you are registered as unemployed and seeking work. Your local Job Centre may be able to direct you towards courses on job application and presentation. You would learn how to submit an application. How to present yourself in a CV. How to conduct yourself during interview. How to tell the story of your experience to date, highlighting points of particular interest to your prospective employer. How to give smart answers to commonly-asked tricky questions.
Anyway, what academic qualifications do you have? What type of work were you doing before you started to care for Dad? With a bit more information we could possibly come up with further suggestions.
Have you considered approaching temping agencies? They have part- and full-time temporary positions for their clients. Once you have done a bit of good work for them they will keep coming back and offering you more. The pay is not brilliant but it is a way to gain the experience required towards more-permanent employment.
Does your fiancée assist in any way? Do you have any relatives who could step in occasionally?
Have you any longer-term plans for your dad? Have you considered him going into a care home? This is not a selfish thought; it could be in the better interests of both of you. You say you need out of the house. As Bowlingbun pointed out, you would lose access to Dad’s council house if he were to go into care. So where would you live?