Putting a three-prong outlet faceplate onto a two-prong outlet box is basically asking for trouble - you'd be creating a safety hazard where someone plugs in a grounded appliance expecting it to be safe, but it's actually not. Don't do that.
The problem that earlier answers touched on is real: your walls probably don't have a ground wire, so you can't just swap the physical outlet. But here's something they didn't mention - even if you somehow got a three-prong outlet installed, you'd be creating a false sense of security. Modern appliances with three-prong plugs expect that ground connection to actually exist. If it doesn't, you've defeated the whole safety feature and now you've got a liability issue on your hands 😬
For a proper fix, you've got a couple real options. You can run new wire with a ground conductor from your breaker box to those outlets - this is doable but involves opening walls or running surface conduit, which is why electricians charge for it. Or you could use GFCI outlets (those ones with the little test/reset buttons) on ungrounded circuits - they actually provide protection without requiring a ground wire and are way cheaper to install. Check with your local electrical codes though, since some jurisdictions have specific rules about this depending on the room and what you're plugging in.