The Gospel and Holy Tradition are very clear on this subject: one can, and should, pray for all needs: physical, psychological, and spiritual.
But I confess I’m like you in this respect. I too have always found it difficult to ask God for something that’s not necessarily going to be ultimately good for a person, and physical health is obviously in this category. One of my former students, now an Orthodox priest, reminded me recently that I had once told him many years ago—when he was suffering from a migraine—that I hoped he got better as soon as he’d learned what he should! I try not to be quite so blunt anymore, or not at least with anyone but myself, but my philosophy on the subject has never changed.
It’s interesting you bring this up just now, given our reading for class tomorrow from Charles Williams (“The Practice of Substituted Love”, He Came Down From Heaven). As you’ll have noticed, Williams speaks of the “dangers” of prayer for the “old self” when it first enters upon the “new way”, and he says some pretty amusing (if frightening!) things about how the ego can manipulate prayer to its own advantage:
“It is with the intention of substituted love that all ‘intercessory’ prayer must be charged, and with care that there is no intention of emotional bullying. Even prayer for the conversion of others is apt to be more like prayer for their conversion to the interceder’s own point of view than to the kingdom.”
Williams goes so far as to claim that it’s even dangerous to pray, however right and proper it might otherwise seem, that a particularly evil malefactor (his example is Nero) not kill his mother (Agrippina). It’s better, claims Williams—”without particularizing”, that is, without telling God exactly what ought to happen—”intensely to recollect Nero and Agrippina ‘in the Lord'”.
This makes excellent sense to me, and my Williamsian solution to the “problem” of intercessory prayer is simply to ask Christ and His Mother to please bless and protect those (by name) whom I know to be suffering while I attempt to hold their specific forms of suffering briefly in mind. Thus, for instance, “Please bless and protect S.” (while thinking of the problem she’s been having with her eye).
This is what Williams has in mind, I believe, when he says that “it [can never] be dangerous to present all pains and distresses … with the utmost desire that Messias [Christ] may be … the complete reconciliation”. More simply put, “Thy will be done.”