After falling for lyk two months I still feel pains at my back and both arms wit neck because I was carrying water on my head.

No one can know without taking X rays.
Some reasons can be simple bruising and muscle strain all the way to something torn, like a tendon or ligament, or even a chipped bone.
The usual treatments are rest, soft pillows but ability to lie flat, warmth, massage, gentle exercise (really just movement to keep a little active), soaking in hot water, refraining from strenuous work, and pain killers like Tylenol. Time and careful attention at home are the only cure.

But you could have injured one of the vertebrae in your neck. If it's just from being swollen and pinching nerves, that will go away. If any of the cushioning fluid leaked out between 2 vertebrae, that needs an X ray and a good doctor.

I agree, you will need a very complete exam with x ray or cat scan and see what injury there was. Also, how was it treated to start with, and did it have time to properly heal.

As was said.. you should have gone to the doctor at least after the pain didn't go away after a couple days... or right away if it was extreme pain. That is if your health really matters to you. That's not being snarky... there are injuries that can be more severe than you might think... or others that can heal badly because they were never properly cared for then they occurred.

We responders need to keep in mind that most of the world doesn't have access to clinics, hospitals, or even doctors the way we do. Although it goes without saying that much of the time it's necessary to see a doctor for what someone is describing, I like to take an extra few minutes to mention a few possibilities about what is going on, either for self help, or to impart a sense of seriousness of the symptoms!