Do my headphones need an amp?

Check two numbers: impedance and sensitivity. Under ~50Ω with healthy sensitivity (100dB/mW+), any phone or interface drives them fine. High-impedance studio classics (150–300Ω) and low-sensitivity planars want a dedicated amp or a stout interface headphone stage to reach level with authority. The tell is simple: if you are at max volume wishing for more, or dynamics feel flat, the amp is the bottleneck — otherwise it is not.