How much do you push yourself?

Here I am again....

Pretty content that I kept my program going. Another upper body strength today and my arms are spent.

I am very aware I easily can injure myself, being in my mid 40s, so I err on the side of caution when choosing weights. As D & K keep saying to challenge yourself, however, I just wonder how much. If I fall out of form, my body will start trying to carry the weight elsewhere (back or neck.) Like what do you do when your arms will just not lift all the way on a lateral lift? Do you immediately drop down on the weight or do you try to push it up (thus falling out of form, using a swinging momentum. etc)

It's the same with HIIT. I adjust and do the low impact version when it is too hard, but I am supposed to push myself, so how much. Sometimes my chest hurts from my heart beating, and I can get light headed occasionally. But I am supposed to burn out during those rounds?

How much do you challenge yourself?