it sounds like your struggling physically, if you sing songs you find hard you wont get better, its like sweep picking on guitar, "the more you make mistakes, the more you "will" make mistakes in the future" Singing isnt like playing the guitar its like playing a violin or cello, there are no frets so you have to learn to feel where the notes are perfectly. My advise would be to find a SLOWER and EASIER song. Also, look on youtube for singing lessons, theres lotsa free ones floating about. I occasionally practice different styles too so i get well rounded, like classical, jazz, pop, metal ect..... Another thing to think about is playing and singing at the same time too, its a big difference, i sound like im being strangled if i play anything that isnt 1 chord per beat xD Screaming, growling, shouting, singing for too long ,singing too high (Which i do alot xD) and singing too loud (i also do alot lol) can damage your voice too SOMETIMES permenantly
You're definitely doing what people call "pulling up chest." It sounds like you're straining A LOT, and it's causing you to lose tonality, power, and definitely pitch. What you're doing should feel kind of like the notes are pushing up against the ceiling in your mouth, so to speak, as though you're either pushing the notes up or reaching for them. If you want to get higher notes, you gotta just let it go, and not struggle to "keep it together." This takes a lot of practice, but it's the general gist of what's gotta go down in order to get those notes.

Also, keep in mind that Kurt didn't really use any good technique to speak of, so if you're emulating his voice, unless you really know what you're doing, you're asking for trouble--and pain.