I don't think it's your aerator. Probably the aerator is adding a bit of resistance to your water flow, which causes the control ball or an O-ring inside the faucet to shift and block the water flow.
I suspect the faucet's control valve is damaged, worn, or obstructed. If it's a decade since it was new or last repaired, I would go ahead and buy a rebuild kit ($15) and replace the components inside the faucet. It's not a difficult job and shouldn't take a first-time amateur more than about 30 minutes to do, especially if you watch a how-to video first.
I also recommend that you buy the silicone lubricant if it's not already part of the kit, since new O-rings in an old faucet will need some extra lubrication.