Poor little thing!

It sounds like her anxiety levels are very high, definitely a good idea to see the GP about it.

I think it is really important to hear out and talk out fears such as these. If you work through it by listening and acknowledging her fears without getting emotional you may get to the bottom of a bigger issue. Just try to remain calm and impartial about her fear.

Have you asked her what she thinks she can do to make sure there are no spiders around? Or to stop the spiders from coming into the house? Sometimes children can come up with incredible solutions that put their minds at ease like putting a magic spell on her bed or even a sign that warns them to stay away! Arcadia's idea of the mosquito net is a good one, involve her in the decision and setting up and she may feel she has more control over it all.

Maybe you could try talking about spiders in stories? I found the story of Charlotte's web a great way to put the whole spider thing into perspective. DDs favorite movie is Charlotte's web (both the animated and film version) and she has a little plastic spider called Charlotte that is a major part of her play. Not that I expect your daughter to be like that... there is something to a healthy respect for spiders, especially when your 3 year old brings a live one to you excitedly claiming it is Charlotte, prompting a discussion about the importance of looking and not touching Charlotte, but I digress...
We talk alot about what spiders do for us and how handy they are to have around to keep all the flies at bay . It has worked so well for us that DD was so afraid of an ant in her room recently and told me to go and get a spider to get rid of it Maybe the movie could be a way for your DD to see spiders in a different light? Charlotte is such a lovely character in the story. You could even read her the book, that way you are there to support her. I would warn her about the story line though, talk her through the it as if she has a deep fear, she may not like to be surprised by the appearance of the spider half way through a movie about a pig!

Also you can talk about how scared spiders are of us! How we are so big to them that they run and hide rather than come to us. That sort of reality might help calm some of her irrational fears that they are coming to her.

Finally, if you are scared of spiders (or anyone around you in the family etc) you might need to work really hard to your fear and your reaction to spiders under control so as not to 'encourage' a response in your DD.

Just keep in mind, her anxiety may not be about spiders at all, they could just provide a focus for her to express her feelings IYKWIM. I hope you can find some answers with your GP.