If you are just starting out, then it takes a while to refine your technique.  It sounds like you need to work on picking accuracy & muting. 

Work torward making your picking as minimal & economical as possible to avoid striking strings unnecessarily.  This tutorial has pentatonic scale exercises that will help you focus on picking accuracy.

https://www.guitartricks.com/tutorial/185

This tutorial is aimed at advanced skill levels, but the lessons on tremolo technique might help you understand what I mean by minimal & economical motion.

https://www.guitartricks.com/tutorial/287 

This lesson is from a tutorial aimed at playing fast lines on the top 2 strings with a gain tone.  But I focus on picking technique in the 3rd lesson.

https://www.guitartricks.com/lesson/14295

Regarding muting, you have to use both hands.

The first thing to do is to maintain constant contact with the strings.  Do not ever release contact with the strings.  As soon as you are done playing a note either play the next note, or at least release enough pressure to stop the note sounding, but maintain contact in order to keep the string from ringing.  Use your picking hand to palm mute the bass strings, or strings lower than than the ones you are picking. 

This tutorial covers muting techniques for both hands.  It mentions beginner, intermediate & advanced skill levels.

https://www.guitartricks.com/tutorial/2281

Playing a different guitar is not necessary going to improve your physical playing skills (your technique).  It's possible you could adjust the action (string height on your acoustic guitar.  And getting an electric might motivate you to practice more.  :)  But focused repetitious practice is the only thing that's going to improve your technique.

Hope that helps!