You must get out a bit. YOU have to stay well and you matter too. I am looking after a sick OH (nothing like as bad as your DH sounds) and my DD always says to me: "You cannot pour from an empty jug", meaning that I cannot look after him if I let myself get exhausted, both emotionally and physically. So I do go out - he has a lifeline pendant and the phone in his pocket.
It must be very disturbing for you to know that his aneurysm could burst - but, as others have said, were this unfortunate event to occur, it would be very speedy indeed and could happen when you are on the loo, or hanging the washing out or whatever. It is important to cling onto some small semblance of normality in this distressing situation.
I am sure that your MacMillan nurse would be able to put you in touch with local carers organisations and schemes to help you get out of the home sometimes. You need this. Sometimes a change of scenery can lift your spirits and help to relieve tiredness.
My OH is under the care of the local hospice: the doctor visits us at home and he goes for various therapies. They offer day and respite care, which we have not yet used. They also offer me therapies and support too - I had a massage from them earlier in the week and it was wonderfully relaxing. I am sure that you could get a referral to your local hospice.
There is one aspect of caring that no-one talks much about and that is guilt. I know this feeling.....supposing he gets ill or dies while I am out, I will feel very bad about being out enjoying myself. I g over and over this in my mind. I have come to terms with this with the help of a counsellor. We have to know ourselves, and you have recognised that you are tired - well done. Now it is time to talk to the nurse and ask what is out there, including assessment by Social Service.
I am sorry your life is so hard at the moment. 