I found the following, not sure if either is your john campbell.
John Campbell
in the U.S. Naturalization Records Indexes, 1794-1995
View U.S. Naturalization Records Indexes, 1794-1995
Name: John Campbell
Age: 27
Birth Location: Scotland
Arrival year: 1818
State: Maryland
Locality, Court: District of Maryland, Circuit and District Courts
John Campbell
in the Philadelphia, Passenger and Immigration Lists, 1800-1850
Philadelphia, Passenger and Immigration Lists, 1800-1850 No Image
Text-only collection
Name: John Campbell
Arrival Date: 5 Aug 1816
Port of Arrival: Philadelphia
Port of Departure: Newry
Ship Name: Brig Wellington
National Archives' Series Number: 425
Microfilm Number: 23
List Number: 174
Newry is in Ireland
1820 United States Federal Census
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View Record
Name
John Campbel
Home in 1820 (City, County, State)
Pittsburgh West Ward, Allegheny, Pennsylvania
Enumeration Date
August 7, 1820
Free White Persons - Males - 26 thru 44
2
Free White Persons - Females - 16 thru 25
1
Free White Persons - Over 25
2
Total Free White Persons
3
Total All Persons - White, Slaves, Colored, Other
3
1820 United States Federal Census
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View Record
Name
John Campbel
Home in 1820 (City, County, State)
Pittsburgh West Ward, Allegheny, Pennsylvania
Enumeration Date
August 7, 1820
Free White Persons - Males - 26 thru 44
2
Free White Persons - Females - 16 thru 25
1
Free White Persons - Over 25
2
Total Free White Persons
3
Total All Persons - White, Slaves, Colored, Other
3
Household Members
Name
John Cambell
Home in 1830 (City, County, State)
Allegheny, Pennsylvania, Allegheny
Free White Persons - Males - 5 thru 9
1
Free White Persons - Males - 10 thru 14
1
Free White Persons - Males - 30 thru 39
1
Free White Persons - Females - 5 thru 9
1
Free White Persons - Females - 20 thru 29
1
Free White Persons - Under 20
3
Free White Persons - 20 thru 49
2
Total Free White Persons
5
Total - All Persons (Free White, Slaves, Free Colored)
5
Household Members