I'm REALLY out of breath at the end of the running intervals, and my run is as slow as I can go without walking. I can get through the intervals and still manage to get a few words out of my mouth, but it takes all I've got.

Just give it some time, as with any training the C25K programme is progressively increasing your challenge, so even if you're drained at the end of these sessions, you're improving your capacity in preparation for the next increase in demand.

I'm not going to encourage you to repeat weeks, but if you do reach a point where you can't complete a step-up of effort then a little consolidation is no bad thing.

Should I get a heart rate monitor to limit how hard I'm pushing myself, or should I just allow my body to do what it will do even if I'm really out of breath?

Personally I'd suggest not using an HRM until you're consistently running 40-45 minute sessions steady state.

The C25K programme is already an interval plan based on time, or distance. HR zone training is a different type of interval marker and if you try to combine the two approaches, as a novice runner, you'll overcomplicate things.

Pin the purchase of the HRM to finishing the programme.