How to sing better? and higher?

So this winter i´m starting a new school after graduating 10th
grade
and there´s a chorus in the school.
so when i went there when there was like a event showing the school
for the new comers and the chorus was singing and at that moment i
fell in love with it .. so wonderful to hear them sing and it looked
so fun ( btw i really like singing so i wanna get better for the
future as well)
so this winter i want to go to the try outs (maybe ) .. i´m really
shy when it comes to talk or sing in front of people so yea..
So now in summer i was gonna try and train my voice and make it
better, making my singing voice better and able to sing higher
atleast. My singing isn't horrible but it isn't that great ether ..
so i need help i at least wanna try and reach my goal and i don´t
want my parents to be paying allot of money for classes so there any
way i can practice at home and see progress after 3 months?
please help > <
(i once was in the school chorus when i was young... tho i didn't put
much effort in then ..)