As dodger says,Try a an aggressive clay the only issue then is you are at great risk of inducing marring on your paint "i have done this many times" which then means you need a good machine polish either by pc or rotary.
It sounds like you have got some paint overspray from some where.
I may be worth just getting it pro detailed.
I myself would not use T-Cut as it will kill your clearcote, if you mis use it.