If you've been riding around with 3 broken spokes, chances are that wheel is junk. If 2 of the spokes are close together, then the good spokes near them have probably overstressed the rim there, at the nipple holes. Also, having loose spoke ends could be pucturing your tube, too. FWIW, not climbing hills in a sufficiently low gear could also over-stress your spokes, causing them to fail prematurely.
Since you ride a low-end bike, anyway, chances are that your wheel a) was never properly tensioned, b) is not made of very durable materials, and c) isn't worth repairing, anyway. Toss it and buy a new wheel.