If you are familiar with AC wiring, please disregard the following, as I don't mean to offend...
Just a comment, but the wiring color code for 110 VAC and 12 VDC is not the same. Most people are familiar with auto 12v
wiring, with red being +12 and black being ground. Did you follow standard AC wiring for the 110 VAC output, which is black is "hot", white is "neutral" and green or green/yellow stripe is safety ground?
If you have a 110 VAC white wire connected to the 12 VDC "chassis ground" (black wire), that is why you are getting shocked. Both black and white 110 VAC wires have voltage on them, and connecting the white wire to ground will probably result in the chassis floating on 110 VAC (a potentially serious safety/electrocution problem).
In a sense, on the 110 VAC wiring, both the black and white wires are "hot", since they alternate polarity, and neither should be connected to the "chassis". That is what the green or green/yellow striped wire is for.
I don't mean to be an alarmist, but the 110 VAC output from even a small inverter can electrocute a person; and if you are unsure if you have a ground fault, you may wish to consult an electrician before having a serious accident.
Inverters are so common now that we forget that they are not like 12 VDC, which usually just throws a few sparks (unless you've ever seen a direct short, which makes things glow and smoke!). And, they can deliver a fatal shock, the same as sticking your finger in a wall socket at home.