Am I entitled to an iphone upgrade?

I have been having problems with my iPhone 4s white. The problem is the battery this is what happed
-20% turns off then when I try to turn it on it's the connect to charger symbol
-i get it to turn on and it's 23%
-I was out with my friend and I had to get it on to phone my dad but it turns off instantly
-I bump it against my hand the back cracks and it turned on at 15% I quickly called my dad but it froze and turned off again
- it turns on all by itself at 6% then turns off instantly

I have had this phone since the 3rd of December I stay in the uk. I then had to take a 50 minute walk home as I couldn't contact my dad.

Also it keeps askin me to sign into iCloud with a random email address and I obviously don't know the password.

What should I do should I email apple, or should I book an appointment at the apple shop?

No you're not.

I don't think you're but you should call service provider and see what's your option.