I went to the hair salon after working.

‘After work’. Or ‘after I finished working’ sound more natural

I enjoyed chatting with mythe hair salon staff.

‘My salon staff’ sounds like you own the hair salon

When I drove to comewas driving back home, a police officer stopped me, h. He checked my alcohol levels.

You could use the word ‘breathalyser’ here to describe the object a police offer would have used.

This was first experience.

Of being stopped, or taking a breathalyser test. It’s not clear

I was excited a little. Of course, I didn't have a problem.

You could also say “I wasn’t over the limit”. Referring to legal alcohol limit to drive