60 psi can hurt you if the stream is just right.
Although 60 psi is within the normal range for residential water pressure.
Although 60 psi can be potentially damaging to some plumbing systems but when the 60 psi is coming through a shower head it should not hurt you.
For compressed air from an air compressor the 60 psi is considered low although it could cause injury to your skin if the 60 psi is directed at your skin and the stream of the 60 psi air is concentrated.
Generally though for water the 60 psi should not cause any harm or injury to you unless the stream is very concentrated and not spread out.
The pressure from a pressure washer can hurt you though as it makes more power.
Pressure washers typically put out pressures which range from 1,300 to over 4,000 psi which can cause injury to the skin if directed at someone.