I understand how you feel. I lived with my father for the last 2 years of his life (he died last April) in order to care for him. I'm an only child, and my husband and I had moved out of the UK 20 years ago, so I came back alone to look after Dad. It is daunting. We had daytime carers in to hoist him for toileting 4 x a day, but other than that, it was just me.
You will not let your father down. Just being with him is what matters most. I used FaceBook to stay in touch with friends and my husband (we also talked on the phone etc.), but basically I just put my head down and got on with it - for Dad. Looking back, it was hard, but at the time I did - and you will do - just what needs to be done. You do it because you love them.
If you ever want to chat with someone who knows what it's like - those times in the small hours of the morning where the sheer weight of responsibility and worry about the future just seem so overwhelming - by all means PM me, I'm always up for a chat or a handhold :)
As for advice - if possible, don't give up your job. You need some life away from your caring role - I didn't have any, and it almost broke me at times. Respite is impossible to get, in my experience - so hang on to as much freedom as you can. I don't feel able to advise re getting help from 'professionals' - it was very hit and miss for me, and all councils are different in what they will and won't do, so I'm not really qualified.
I really feel for you, and for your father. I take comfort in knowing that I did all I could, and Dad knew I was there for him, and he died at home, as he'd wished. It really is a tough thing to go through, though. I wish I could help.