I actualy used to be this same way...alwasy trying to block out nosie...trying to sleep in silence....getting frustrated...and mad when i was woken up...
however I have discovered to learn to embrace it.....who cares about dumb little noises.....now i actualy sleep better with nosie then in silence!!!

OK well, here is a way to get urself to sleeping with noise.....get a fan or if u have a fishtank even better.....
the key is to not try to make everything quiet but to make everything louder around you so little nosies don't seem like loud ones..
for example a fan is a easy trick.....get a fan and turn it on medium.....point it at the ceiling....and just leave it on indeafinitly.....ur mind will get used to always hearing it.....so u can go to sleep but all outside noise will not seem that much of a bother because the fan is drowing it all out for you!!!
trust me it works!
it creates a new silence is a sense.....it very peaceful.....u don't here little dumb noises any more 8)
You can also try leaving the TV on at a lower volume....like on a boring station..like the weather channel or informercial....I find that I dream better when the TV is on.....because of the light changes and noise keeps me closer to conciousness.

its just a matter of training ur body to except your environment...its much healthier then manipulating it or blocking it out.