Where is the boil? Where are you shaving? How are you 'unwell?'
A boil doesn't mean staph or other bacterial infection. Keep an eye on it, keep it clean, wash well if it opens up, see a doctor if it gets infected or smells.
Being generally unhealthy can mean more likelihood of skin infections, yes. Infections do get in through cuts, scratches, or even insect bite holes. Wash well with soap and rinse well. Apply an all purpose anti-bacterial cream like Neosporin. Stop shaving!
A staph or strep infection like cellulitis spreads a red rash very quickly. You will be able to see it very clearly. Rarely it won't be as visible if someplace like in an ear.