There never was such an incident regarding Trotsky of less than blessed memory. He was never in any yeshiva and did not come from a frum family.
An MO school will not help because it will be too hard to adjust to a completely different framework for someone who has already had adjustment issues.
The rav was not right in throwing you out. How in the world did he find out you were talking to girls? I really have no respect for any rav or menahel who takes the word of a snitch – or even if he does, he should take it as a reason to work with you and not to throw you out. Someone once snitched on me to my public school teacher in the 6th grade – and I was actually guilty as charged – but the teacher disciplined the snitch for being immature and I had the last laugh. Today, that teacher is enjoying his retirement in Florida after a second career as a very successful real estate broker.
There are probably other bochurim in your yeshiva who get away with more than you were thrown out for – because they are fakers and know how to hide their aveirois, or because their parents are (wealthy, big names etc). Throwing out should be reserved for bochurim who disrupt, or who really need to be in a vocational framework, or who are truly OTD and convincing others to go off.