Is my phone locked if it doesn't have a SIM card?

My iPhone 4s does not have a SIM card. My carrier is Boost Mobile, which is owned by Sprint.

Does that mean the phone is locked?

Can I buy an unlocked phone and make it work with my carrier?

No SIM does not mean locked. That's a matter of configuration.

Your phone is not locked, but your phone does not need to be locked. "Locked" in this case means carrier locked for a GSM phone. You have a CDMA phone, which is tied to Boost and only Boost. Adding a SIM card (even if it has a slot) won't do anything at all for you.

Your phone would have to be "flashed", meaning having the firmware that runs it rewritten to work on another carrier. Lots of places used to do this, but it only works for other CDMA carriers (Sprint, Boost, Verizon, Virgin, other regional carriers). You can't use your phone on a GSM network at all. It doesn't have the hardware to run on those.