It does sound like a Shrike. It should have what could be described as a black mask across the eyes.
Sometimes at first distant glance it is mistaken for a Mockingbird. However, it has the mask, wings blacker, and bill is hooked. The Northern Shrike is the same size as a Mockingbird and the Loggerhead Shrike is slightly smaller.
The common Shrike down here, is the Loggerhead. It usually flies very fast and low which is different from the Mockingbird. It usually won't let you get as close as a Mockingbird will either and it is not a singer like the Mockingbird either.