This fear really started when you first thought of bugs as 'Eeww'. Then you practiced this thought until it became a fear. Now you see a bug and you panic and scream. another habbit you have been practicing, so now, it is the only way you know how to react when you spot a bug or spider. Think of this like brainwashing yourself into fearing bugs. There is treatment like CBT therapy to undo this. You need to change the way you think about these critters, starting with learning to control your panic. you need to change the conditioned response you have developed. You don't have to kill bugs, worry about that when you can handle bugs.
Your mum is right in thinking bugs are a friend, and there are lots of good bugs that many people even love. You are right in that you are not going to turn this off like a light switch, it can take time, and not easy at first to learn a little about bugs and get familiar with them. Many bugs you find are just household pests, not harmful in the slightest, just a pest. Some are bloodsuckers and a nuisance, and a few can sting or bite. You see a wasp near you, you panic, start swatting at it, that is a good way to get stung.
You find a bug crawling on you and "SHIVERS". the feeling is a lot different if you pick up a bug and let it crawl on your hands. Learn a little about insects and spiders. Where you can, just become familiar with them. Find a bug fair or reptile convention near you and go. You can talk to people just like you but keep such critters for pets. they would be happy to talk to you about bugs and spiders, perhaps even hold something like a preying mantis or big spider. It take a lot of will power and determination to overcome your fears, but it certainly is possible. I grew up with all sorts of bugs, spiders, and flying insects about, and I usually played with them. It would make my day if I could get a big darner fly to land on my finger, and I have attracted wasps to my hand with bits of fruit. a small house spider crawling by, and I pick it up for a photo before putting it on the wall out of harms way.
It is all a matter of changing the way you think of bugs, learning a little, and becoming familiar with and learning to trust such critters:
https://www.flickr.com/photos/32083154@N02/15245718390/
https://www.flickr.com/photos/32083154@N02/9767704716/
https://www.flickr.com/photos/32083154@N02/3710691068/
Godspeed.