[Antoninus]

I value their prayers, but I also know that God has a plan for my life. If that plan includes healing, hey,I’m all for it. If it isn’t, He will give me the grace to go through life without it.

The question is not whether you value their prayers. It's whether God values their prayers. If not, why do you ask them to pray for you? Seems like it would be a big waste of time to me.

[Dr. Eckleburg]

Of course God "values their prayers." We are commanded to pray for our own lives and the lives our our brethren.

That command, however, does not negate the preeminent fact that God knows our prayers; God knows what we need; God gives us everything we have; and God alone heals the sick.

If you believe other people heal you by their prayers then all I can say is perhaps your priorities are skewed.