Ok, well there are a few issues.
As the previous poster has said, you should not be expected to be 'flying solo' this early on. A reputable company would not expect this and it is important for you to remember that the way you are feeling is caused by the lack of appropriate induction, training and support you have received.
The fact that you are worrying/ thinking excessively about work outside work hours probably indicated that you are just the sort of person who has what it takes to be a good care worker. care professional!! Ie you think about the work you are doing, the quality of service your clients recieve and how well you are able to provide it!! Part of my job is in commisioning Dom care packages and we love staff like you!!
Also there is in any new job a period of adjustment especually if it is relatively new to you and more so if you have been out of the job market for a while. As long as the correct support is in place it DOES get easier, you become more confident and comfortable and switching off happens much more naturally.
I suppose you have two options open to you, either stick it out with this copany but ask to meet your manager, calmly point out that whilst you are commited and keen to do a good job you will need a bit more support in this early phase with the company. Ask if they can give you some additional specifc training (ie hoisting, manual handling etc etc) and maybe pair you with an experienced carer for a few weeks. If they are halfway decent they will facilitate this.
OR you could look for a similar opening elsewhere. If you go on the CQC website (care quality commision) you can serach for any prispective agency and look at how well they have done when inspection took place. hey look at things like staff training, any complaints regsitered, lots of things.
Happy to try to answer any other questions you may have, Good luck!