Are medical records private? Can someone who was diagnoised with
borderline personlity disorder work in the criminal justice field
after completing their bachlor's degree in criminal justice or would
they be turned away?

Although your chosen username suggests that, you didn't say where you
were from (San Diego CA?). It is possible that there are variations
between different jurisdictions; it is also possible that it depends
on the workplace. Several hypothetical cases:
(1) Candidates are asked to sign a statement that they don't/have
never suffered of psychiatric problems : if you sign it, you gave a
false statement, if you refuse, you won't get hired;
(2) Candidates are asked to sign a statement giving them access to
their medical records;
(3) Candidates are asked to go through psychological evaluation. 

I am not sure, by the way, but discrimination against you because of
borderline personality, unless it is a place where special conditions
apply (e.g., intelligence community, other extra-sensitive places),
might be - if you're in the United States - unconstitutional.

The criminal legal field is also very wide: Do you want to be a
solicitor (lawyer)? A paralegal? A court marshall?

I want to be a Juvenile Probabtion Officer