You should always ask about migration help before buying a new hosting plan. However if you still need any help in migrating your wordpress site then you should hire some one for this small task. it will cost you no more then $5.
other wise good luck for you if anyone can help you move the data free for you
PS: you have to follow the following basic steps in data moving
1. login to your old cPanel account and make backup of your MySQL database by going to phpMyAdmin
2. open file manager or FTP and download all the files to your local pc
3. open your new hosting FTP or file manager and upload all the wordpress files.
4. create a new Database in your new cPanel i,e DataBase Name, Database User, DataBase password.
5. put this new Data Base details in your WordPress configuration file which is https://codex.wordpress.org/Installing_WordPress#Step_3:_Set_up_wp-config.php
6. import the old database which you have downloaded from your previous provider TO the newly created database.
if you don't understand any thing then GOOGLE it. or hire someone and pay him some money.
Cheers