I feel like there is a pill lodged in my throat could it still be after a day?

Possibly. The pill may be stuck or sticking in the esophagus. Depending on the pill, it can be caustic and eroding the lining of the esophagus and can lead to a major and serious condition. The pill may still be there a day later. Make sure to take pills with plenty of water and stay upright for 30-45 mins after (some meds even longer - ie fosamax) if persists or worsens - see your doctor.