At 4 months, mouthing everything and gum discomfort can be an early teething sign, even before a tooth is actually visible. The safest kind of teether is a firm, one-piece silicone or rubber design with no small or detachable parts, big enough that she can't fit the whole thing in her mouth.
Next Steps
Chill it in the fridge, not the freezer, before giving it to her, and always supervise while she's using it. Wash it after every use with warm water.
Health Tips
If she develops fever, refuses feeds, or seems unusually unwell rather than just fussy, please consult her paediatrician.