Okay...So I'm good with scales and soloing but...

When I solo with distortion
and I move from one string to another
I get a lot of noise

For Example:
I've been learning Marquee Moon by Television
and
when I get to the pre-chorus
I do the lick
but
once I move on to the next string
I can still hear the other string that I just
so
obviously
when you have distortion and that happens
it gets really messy

Anybody has helpful tips?

You have got to let go of the string gently so that your finger mutes the string before letting go. Just about everything you play you have got to be good at muting.

Learning how to mute strings when playing a lead passage involving string skipping is a subtle but absolutely necessary technique to learn. A piece of music that really helped me with this was the first solo to GNR's version of Knockin' on Heaven's Door.

A lot of younger players get what I call "speeeeeed syndrome" when younger guys get into metal they want to play a million miles per hour and that's all they want to do. I predict you fall into this category. Its not a bad thing at all. Just something you will have to work on. It's just that your speed has developed faster than your technique has. You've skipped over the small things like string muting and the subtle touches of playing clean... Work on the runs at slower speeds keeping the time right... just at a slower bpm... play it as clean as possible then move up. Don't move onto another speed until you can play it clean at the speed you have it at. This exercise works well for all types of music. You will get it, just practice!!! Good Luck

Try the following basic exercise, it is not in any specific key. If you know your scales you can apply the same fingering to scalar patterns and go up and down the fretboard in 2.5 octave runs. This excercise helps to get picking accuracy, clarity and improves overall technique.

123
---123
------123
---------123
------------123
etc and

1234
----1234
--------1234
------------1234
----------------1234
etc

Just play the pattern up and down. As it is just a basic pattern you can concentrate on the technique without getting bogged down trying to remember a complex run or riff.

The important things to concentrate on are:
Alternate picking - up down picking for each individual note, plenty of info on this site
Muting - practise dampening the the strings with the heel of your picking hane AND with the fingers of your fingering hand. There is no one technique for anyone, it depends on your own style, length of your fingers, dexterity etc.
Try to pick evenly from note to note and string to string with the above in mind and pretty soon you should be able to eliminate those background noises. Everyone finds this difficult at the beginning but you will get around it soon enough.

One thing I forgot to mention, it's something I learnt from the Michael Angelo Battio instructional dvd "Speed Kills".

Get your plectrum and play one note as fast as you can with a perfectly even rhythm (it doesnt matter how fast it is, the most importnat thing is that it is comfortable for your hand and that you can play it for a long time without losing tempo). Now look at how you are holding your plectrum and how your hand rests on the strings. Make the necessary adjustments to ensure that you can play the same speed and keep unused strings muffled. This is your "maximum picking ability" (for now).

Everything you play from now on should be based on the exact technique you personally use to hit your top speed. So even if you are playing the 123 exercise at one note every 2 seconds your picking hand is moving in exactly the same way as if you were playing 16 notes per second. A lot of players starting out lose clarity when they up the speed of their picking becasue they change their technique. Stick with one hand position from the start, it will improve your ability by 200%.

Picking speed will increase with practise, getting the left hand in sync is what the 123/1234 exercise is all about.
Best of luck