Yes, it's pure, unadulterated anxiety. More importantly, you need to realise that this is now at a stage where it's about to start impacting on your daughter's life and well being, not just yours, so you either need to learn to control it, or deal with it in another way.
I have spent the vast majority of the last 47 years being severely arachnophobic. I tried all sorts of things to get over it, hypnosis, self help, London Zoo Friendly Spider Programme, everything, but I couldn't even get close to a dead spider embedded in perspex, let alone a love one. Unfortunately, Little Unicorn 3 picked up on this behaviour and developed the same fear through imitation. One of the worst things to happen was her being in tears from sheer terror of seeing a 1cm spider in the kitchen with me, her 6ft knife wielding surgeon father, also frozen to the spot and unable to do anything. That was the day I decided that I had to get over my phobia no matter what it took. I needed a psychotherapist and some serious effort with EMDR, but it worked - I still don't like them, but I can now deal with them. Massive harvest spiders run away from me now, not the other way round!
I'm afraid that if you don't do something about your anxiety, you'll be at risk of either passing your anxiety to your daughter, which is bad enough, or, far worse, cause a huge amount of resentment and rebellious behaviour against your anxiety driven highly restrictive parenting. I can assure you that neither are good options.
For your own and your daughter's sake, please consider getting some help with your anxiety issues if it's a recurring problem. Life is much more pleasant when you're not anxious all the time.
Hope you and your daughter are both ok.