Seems to me you need lower gearing on your bike. Either that or slow down your cadence to the point where you can still breathe as you climb. If those options don't sound appealing, then yeah, stop and catch your breath. No one on this forum wants you to keel over and drop dead
Okay, there is another option that worked in my particular case on a similarly intimidating hill -- I lost some weight. The hill is quite a bit easier to climb now