What im not getting is that its not written DPI on my screen. It says resolution. So thats the same thing ?
Sorry, yes, I meant "Resolution" (message editted to say that now).
If I just change the resolution to 300 instead of 100 it actually bring the image bigger and I cannot see loss of quality even at 100% size. Question is: resolution = dpi 
The reason I suggested starting with a new document is that some people get mixed up with a couple options that PS has when you resize an image's resolution. There is an option call "
Resample Image". If you do not have that checked on, then PS does not change your actual graphics. All it does is set the document settings to "300" dpi
which only affects printing.
If you don't understand this, do a test. Print your 100dpi image on your regular printer. Then change the resolution to 300, with Resample Image NOT checked on. In PS your image will look the same n your monitor. Now print it out again. You will see it prints out 3 times smaller than it did before. That's because the printer is now cramming in 300 pixels per inch.
So, you need to check on Resample Image, set the res to 300, THEN go in the document size and set it to the correct width and height in inches.
PS will then stretch the graphics to fit the correct size.