Op, you sound just like my DM when she doesn't take her meds. She too thinks she isn't paranoid.
As for the chicken pox, the younger the child is, the milder the symptoms. And to add, I was 6 weeks old when I had it back in the early 80's. My DC had it last year. My youngest coped better than my eldest.
In your area there should be a mental health crisis team. Please contact them and tell them you feel that you and your DD are going to contract cp and die. They will take you seriously, not because you and your DD are going to die, but because you are ill, mentally. You need professional help and medication. The meds will help you cope when your wanker dh is away.
If you don't learn to identify to warning signs, it will only take you longer to get better and you may even be sectioned. If you work with the mental health team, they will not section you unless you are a danger to yourself or anyone else. Trust me, I had to fight to get my DM sectioned. She was talking about saying her goodbyes and I went mental on the phone at the team.
You also need to show your dh this thread. At the least, show him my post. Because your dh sounds like my dad. Prefers to put his head in the sand than look after my DM. As a result, she isn't able to live a normal life. She can barely go out. She has constant paranoid thoughts and her and my dad don't have a normal relationship. They don't go out, they don't have holidays etc. And I don't have a normal mother daughter relationship that other people have. I can't leave my DC with her, because the meds now are so strong (think 40 years of damage done) she isn't able to. I can't go shopping with her, go out for lunch with her. I couldn't even take her wedding dress shopping because she can't stand being around other people. She also left my wedding early because her anxiety went through the roof.
So please, please seek help for how you are feeling now. Because once the chicken pox issue has gone, your anxiety will still be there and you will find something else to focus on.