Sounds like you have a Model 43, 47 or 51 Hamilton, depending on features. Except for the Model 51, Hamilton rifles used a rifled brass barrel liner in a barrel jacket - the barrel of the Model 51 was steel and screwed into the reciever. The Model 43 is cocked by pulling the bolt handle back and has a rounded stock. The Model 47 has a stricker knob and a board stock. All should be marked as to Model on the barrel. If you can find Grant's "Boys' Single-shot Rifles" there is a discussion of all Hamilton rifles.
Bill