One way to make sure that you are singing the right pitch is to listen to yourself as you sing. No we do not mean record yourself but you can take advantage of this daily vocal exercise. Sing the Solfege every day and do it without the help of an instrument such as the piano.
The vocal exercise should help train your voice while training your ears. Listen to every note that you hit carefully. This improves how you sing even in the absence of your instrument.