Please don't feel guilty. I was a carer for my mother for many years and it can be exhausting. Everyone needs a break and some help to get through it. My daughter was amazing during my cancer diagnosis and treatment but I could see she was worn out. The thing is that, as a carer, it can be a 24 hour job, and that's not sustainable. It was the right decision for you to make that appointment and I'm glad your GP was helpful and listened. I hope the medication helps but you can get further help too. CRUK has some has more information on where carers can get support. 
My daughter is currently away for a couple of days staying with a friend, content in knowing that I'm being looked after. It took some persuading for her to go, but it's good for both of us.
Please take care of yourself and don't worry about needing support. It's something we all need. Take care. Gill xx