Counseling with a clinical psychologist that specializes in animal phobias may be your best option.
Therapy is not what you fantasize it to be. It is easier than you may think.
Killing spiders is not going to help your fear at all.
Here is a response I gave for a person asking how they may overcome this, I hope it helps:
First, you have to understand your fear and what it is.
This is a mental conditioning, like brainwashing yourself into fearing spiders. this would start the first time you ever feared spiders, or something you learned from perhaps parents that feared them.
The lack of familiarity and knowledge plays a big part, and growing up, you hear all the horror stories, urban myths, and hyperbole about spiders. Not knowing better, when you see a spider, you let fear take control. You practice this repeatedly, and dwell on your fear until this becomes subconscious.
A bit like memorizing lyrics to a song. you dwell on these thoughts, until they are no longer conscious.
You can overcome this, but first you are going to have to change the way you think about spiders.
Preferably, not thinking about them at all, and just ignoring them.
Everything you think you know about spiders is false, especially little horror scenarios you fantasize in your mind, like they will jump on you or bite if one is crawling on you.Nothing is further from the truth.
You are going to have to have enough will power and determination to become familiar with spiders.
You are probably not afraid of your pet cat because you are familiar with it. It is the same for spiders.
Learning a little about spiders helps a lot and you might even find this interesting.
Read about their anatomy.
Look at photos of spiders, and how different they can be. Some can look intimidating, some actually cute. Watch videos of spiders and how they behave. Get to 'know' them.
If you can confront your fear with a little will power, catch one in a jar, watch it and observe it.
Think of it more like a pet than some demon that wants to harm you. Take it outside and set it free.
Even this will give you a sense of accomplishment. you will feel anxiety, but don't push yourself so fast as to panic and give in to your fear, you have to chip away at it a little at a time.
Right now, the last thing you may think you would ever do is let a spider crawl on you.
I grew up playing with all sorts of spiders, and no one told me I had to be afraid of them.
I liked spiders because they were different than other bugs, and over the years, I have handled thousands of them. small ones, big ones, fast ones, and docile ones.A few times, even dangerous ones. Most, simply don't bite, some can, but I have never been bitten where it wasn't my fault, usually from trapping the spider between my fingers. None were no more than just another 'bug bite'. Maybe like an ant sting.
A good place you might start, is to uncover some truth about spiders, and dispel some of the awful stories you likely believe. Here is an interesting site, loaded with things you never knew about spiders:
http://www.burkemuseum.org/spidermyth/index.html