with advancing pregnancy
as the uterus
grows it will cause pressure on pelvic organs and as you are having the fetal head down it will also exert pressure so you will feel like pushing,
but if your braxton hicks contractions
become severe and recurrent you have to consult gynecologist as early as possible,
your discharge could be physiological leuchorrhea of pregnancy but if that is associated with smell or itching or if that becomes clear like water etc better to get examined once.