Akash- This is a tough question! I wish I had a time line or a definite idea of an end point for you, I'm still hacking out this jungle myself.

My PT seems to be of the mind that the constant cramping sort of thing, while crappy, Can have its benefits in that your muscle isn't atrophying even though it's hard to control. There is still Some signal getting through to it. I guess it really depends on how damaged you LTN is, and how long ago the injury was. There are surgeries where docs transfer the thoracodorsal nerve to the serratus anterior to make it work again, but that's usually done when it's palsied.
When that muscles Does start freaking out, especially if you had a traumatic injury associated with it, it throws your body in to this weird hell cycle. LTN injury causes scapular winging and trouble holding the shoulder up> shoulder rolls forward compressing brachial plexus and straining compensating neck muscles> narrowed brachial plexus/over worked neck compresses and irritates the nerves that hold your shoulder up. Rinse, repeat, lay on the floor in pain.
With your other familiar symptoms though, it's probably a good idea to pursue docs or PT focusing on a brachial plexus injury or compression, even an atypical TOS presentation (I'm going through this battle right now). The LTN goes through the scalenus medius and hypertrophy or spasming really irritates it. Especially if your neck stabilizers are injured, making it very likely you've developed a kyphotic posture or are just over working your scalenes to make up for it. A lot of the TOS treatment deal with mainly the Anterior scalene which, in my experience, does jack all for helping the LTN symptoms.
My serratus freaks out whenever I try and lift my arm, and my PT helped confirm that this was from my initial guarding behavior of the injured arm and without the resistence and pull of my serratus anterior my levator scapulae and neck muscles were doing all the lifting for me. They're just not built for that kinda work!

Def go see somebody, someone who specializes in posture physical therapy if possible too. Most PT's will put you through the paces of strengthening your rhomboids and upper traps to make up for your wacky serratus anterior, which may work for you if you haven't tried it. Lots of core strengthening and mid back exercises as well.
All the winged scapula specific work in my case wound up only further irritating the neck and shoulder support muscles causing a lot more dysfunction, but the core work did make it so I have Amazing abs for a shut in, Hahaha. Still, everyone on here has such a unique injury and background, just cause something fails for one person doesn't mean it won't be the key to relief for another. Try to keep zen about it though and be pushy with your PT if it's not working.