Consider the following points. You search the entire line, rather than the artist name, example data:

Seamus McGuire:The Wishing Tree:09-14-2000:14.95
Foo:Bar:01-01-2000:15.00
Bar:Baz:01-01-2000:150.00
[download]

Searching for Bar:

Entery Either First or Last name of the artist:-1 to quite>Bar
Artist Name:Foo
CD title:Bar
Date:01-01-2000
Price:$15.00

Artist Name:Bar
CD title:Baz
Date:01-01-2000
Price:$15.00

Entery Either First or Last name of the artist:-1 to quite>
[download]

To resolve this split the line into individual fields and match on the artist name only. You could also remove the $flag variable and just add an else to your if. Note that currently your searches are case sensitive. I know OP was not very specific when posting, but many people tend not to consider case to when using search interfaces. A slightly amended prompt:

print "Enter either First or Last name of the artist:-1 to quit> ";
[download]

Now here's the interesting part, restart the program and search for "Bar" twice:

Entery Either First or Last name of the artist:-1 to quite>Bar
Artist Name:Foo
CD title:Bar
Date:01-01-2000
Price:$15.00

Artist Name:Bar
CD title:Baz
Date:01-01-2000
Price:$150.00

Entery Either First or Last name of the artist:-1 to quite>Bar
Artist not found
Entery Either First or Last name of the artist:-1 to quite>
[download]

I'll leave this as an excercise for you :)

Update: Strike out nonsense, the pitfalls of my poor multi tasking.