Do I have to tell my employer about my military service?

I was discharged during boot camp due to medical condition. I still want to serve and talked to recruiters from all branches but everyone says its a no go except for air force they said its a maybe. I would also like to join law enforcement but am wondering if i have to even tell them that i went to bootcamp or joined the Navy at all? While being discharged from the Navy someone told me that since i didnt finish boot camp its technically considered as if i never joined the military. Is this true? and if so can i get away with just telling law enforcement agencies that i never joined the service?

While i was in i told my chief i was depressed and i missed my family and they separated me because of it. They told me i had traumatic stress disorder and sent me home after being in separations for 3 weeks.

Thank you all!