If it was running fine before you changed the oil & if the dipstick reads full & if the new oil filter is tightly sealed & you didn't do anything else but an oil service I'd start it again and let it run. If the sound doesn't go away after 15-30 seconds shut it off, there's another problem. To me it just sounds like the oil just needs a couple seconds to start pumping again.
In the future, change the oil while its hot, and then start the car when the service is done, it has always worked for me.
Let me know how it turns out.

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Thanks,
Dave

1998 BMW 540i Sport
1995 E320
1992 400E
1989 BMW M3
1979 Triumph TR7 (1st car)
1986 BMW 735i (Sold)
1980 BMW 320i (Sold)