Why am I only getting sound from the headphone jack?

Inside the headphone jack is usually some kind of trigger or sensor so the phone knows that headphones are plugged in. If the headphone jack gets dirty, this trigger may not un-press so the phone will think there are still headphones plugged in. Try cleaning out the jack with some compressed air, or if that doesn't work, use some isopropyl alcohol on a q-tip or toothbrush. Make sure you let any alcohol dry off before plugging anything into the jack. Also make sure the phone is off before you go poking around with liquids in your phone!

If this is happening repeatedly, there may be a problem inside the headphone jack and you might need to replace it. There's a guide for that here.