I just want advice for the conversion I just did before I plug it all in.

Details:
1. I have a two-phase 220V Sears Craftsman compressor which uses a 220 volt
plug with one blade sideways (otherwise it looks like a normal 120V
grounded plug).

2. I have no sockets in the house which fit that 220 volt plug.

3. I have a three-pronged dryer socket in the garage with 220 volts (two
hots and a neutral).

4. I just attached a new 3-pronged male dryer cord to a female 220 volt
plug with the one blade sideways.

Before I plug in the compressor to the recepticle to the dryer cord to the
recepticle, would you have any concerns about safety or other?

I assumed the neutral in the compressor plug was the center wire (looks
like a ground pin) while I assumed the neutral on the 3-pronged dryer cord
is the L-shaped center pin. Is that the correct assumption for the shared
neutral?