Personally, I'd ditch the guilt, take a deep breath and make an appointment. I think it is important that your support team know how much you are struggling and would want to support you. It might also be useful to ask for a referral for some counselling, talking therapies can be a great help and it sounds like you might also be struggling with exhaustion/depression, which wouldn't be at all surprising from what you have described.
Sending you a virtual hug - sounds like you need one. Don't worry about sorting it all out - a step at a time...
Good luck, Sarah and it would be good to hear how you are getting on - even if you don't feel ready to make changes.
Update...
Glad to hear you have taken the plunge and contacted the practice but sorry to hear that the practice nurse is not being helpful. Persevere . Personally, I'd make an appointment to see the GP to discuss your options and see if he can hurry this referral along. It might also be worth asking if there is any help for carers, even a coffee with a local carers group can make a difference. You need a support network, online and offline, by the sounds of it.