Electrical issues cause car to struggle

While driving, my car started to die, but did not die completely; instead, whenever I pushed on the gas, it would start to rev up like normal, then die, then rev up again, then die again, etc. It never got up past 25mph between the revving and dying down. I was able to drive it 3/4 of a mile back home successfully.

A few days prior, my battery light came on. I've also had intermittent spouts of the windsheild wipers turning on in breif spurts without being engaged. I am leery to call this a battery problem because it died while driving, but do not know what else it could be. Maybe alternator? Maybe wiring? Any help would be greatly appreciated, thanks!