A/C compressor leaking oil

My A/C quit working yesterday while in stop-and-go traffic in Texas traffic. Outside temperature was ninety eight degrees. It seemed to work in the morning and evening when temperatures were lower.

I thought that the compressor, clutch, pressure switches were working since the A/C seemed cool in the evening. This morning I bought a replacement kit of 134a. When I hooked it up the pressure was within limits but on the low end. I added the 134a when the engine was idling, not revved so I added most of the can over a period of several minutes.

After a while I heard the compressor kicking in and out which meant that it had not been before. It would kick in and run for about one second, kick out and repeat every seven seconds or so.

After that the A/C was definitely only blowing hot air and I could hear the compressor continuing to cycle on and off, never actually running when the clutch kicked in.

I just went back out to check some more and discovered a patch of oil on the ground. I think this must be compressor oil? Did I blow up my compressor or is this the oil from the added 134a leaking out?

What is the best way to test the compressor? Thanks!