Is there any possible way I can hide my Twitter profile from people who aren't logged in?

[Jack]

I've just finished my first college year and after having a dreadful year that's been nothing but trouble, I saw them advertising the college on TV yesterday and one course mentioned was mine. Therefore I tweeted about it, and said the boy will finish scarred for life like myself.
Well I didn't tweet it directly to college but they found it, tweeted back to me "why are you scarred for life?" And I basically put back it's been a shocker of a year basically.

Then my mum had a phone call from my old head of department saying I'd been tweeting about them. I basically just had a small lecture on how I shouldn't post things like that and then that ended. I deleted the tweet and any other they may found offensive, and I know I shouldn't have posted anything and I learnt my lesson, but with the shocker of the year I had I just needed to vent it out on Twitter.

Anyway now I just have this feeling I'm going to get monitored more often by them now and I don't exactly want to be watched what I post in that way. I know if I block them then they can log out and view my feed anyway, but I don't want to make my account strictly private to approval.

Is there a way I can only make it visible to people who are logged in? If so, how?

[Dunson41]

Twitter is your annoying voice to the world, don't tweet stuff you dont want people to read.

Use facebook or something.