Hibs you want something that's not going to solve the problem that you have, no matter what does or does not show up on the bill, the time of the call is what is going to have you parents asking who you have been talking to so often from a number that is blocked or not showing up.
So in YOUR particular case, your options are very few, and they are in order..
LIE
Use someone else's phone to talk to the people your parents do not wish you to talk to.
Talk to them anyway and deal with what happens when you do.
Get your own phone in your own name, and start paying for your own apartment, food, bills, you know... life in general.
Those four options pretty much cover it I think.
There is of course a 5th option, but I know you would not care to hear abotu that one, but here it is anyway.
Give up the cell phone and talk to them using pay phones.