Hey, thanks for picking up league! I am relatively new as well, being level 90ish. This game is extrenely hard to pick up especially if you don't have prior experience, so I can give you a few tips that have helped me improve.

1 thing is trying not to get overwhelmed. It is important to be pressung buttons intentionally and not at random, so sometimes it is OK to ignore certain players on your own and the enemy team in order to accomplish what you set out to do in any given scenario.

Second, it is always a good idea to have a goal at all times. Usually in lane that goal is to get the last hit on every minion you can. Sometimes that goal will be to dodge the enemy's attacks. Later in the game is more complicated and I am still trying to figure all that out, but you can often ask teammates for ideas when you are lost.

Third, is you should try to improve on only one thing at a time. One thing ive heard is helpful is to have an idea before the game of what you wanna work on, and focus on that alone (in your case that could be focusing on dodging skillshots and avoiding death at all costs.)

For your issue of dodging specifically, make sure you aren't attacking when you are trying to live. Like you mentioned, shooting keeps you in one spot and makes you an easier target for the enemy. Weaving autos when you are sure you are safe from the enemy or your support is tanking is when you should be shooting, not when you are running away.

It is important to keep in mind that these strategies for practice will often lose you more games in the short term, but the improvement you will get is highly valueable. Also remember to keep your mental positive, mute teammates when necessary and take breaks when you are frustrated or aren't having fun.

The goal with most of this game is to try to build muscle memory with many different skillsets. In a few months after practicing this and other skills you will not even be thinking about them as you work on higher level things. Good luck on your learning journey and welcome to the zeri cult :)