When you say ‘school’ are you talking about college/university?
You have said ‘school’ many times here:
“…dismissed from school…”, ** meaning first institution **
“…transferred to another school…”, ** meaning present institution **
“The school only has a letter stating why I was dismissed.” ** present institution **
One type of issue comes to mind if you are talking about college or university dismissal and the potential resultant weight of that dismissal for the reasons you stated: matters related to public indecency.
There are so many things to consider regarding your undergraduate institution’s duty and responsibility to a referring institution where close group work with other young adults is going to be a necessary part of the graduate student’s duties.
Were you seeking to enter the teaching professions, or law or medicine (ultimately), any actions known to the undergraduate institution which might be tantamount to public indecency, though not referred to the authorities and handled exclusive within the environs of the campus administrative system, would seem necessary to be disclosed.
Have you inquired of the current institution exactly what action they will take when sending your transcript forward for graduate school admission, and have you spoken with an advisor?