3.7V is the average voltage of a discharging Lithium rechargeable battery cell. It is ruined if it is discharged to below about 3.2V so you need a circuit to detect the voltage of each cell and disconnect the load when one cell drops below 3.2V.
Of course your battery needs a charger designed for a Lithium battery. Each cell is 4.2V when fully charged and when the charging current has dropped.
Another problem is no-name-brand Lithium 18650 battery cells from ebay. Some are fakes: