There are a couple things going on here. First, scholars--good ones--have used "anxiety" as a blanket, uncritical explanation for all sorts of social development and change, especially in the late Middle Ages. The fifteenth century is a prime example. The Reformation happened in the sixteenth, so clearly, the entire population must have been desperately anxious over having to "work for" salvation (bit o' projection from a particular portion of the life of a single Augustinian monk) and thus they fled eagerly to the Lutheran message when it was proclaimed. First problem here: large chunks of Europe, including areas very much exposed to Luther's preaching, stayed Catholic. Second problem: More recent research has shown that 15th century Christians were pretty happy with their religion, if not always with individual clerics in specific times and places.

Second, we need to be really cautious about projecting backwards--or sideways--a "simpler life" idealism. I think holy crap how do I feed my family when the crops haven't grown for three years and shit the English are torching our fields is as legitimate a source of bad feelings as technolust, Facebook competition, etc. Jewish legal decisions and decrees from medieval Ashkenaz (ETA: northeastern France/German Rhineland) are filled with exhortations to parents to stop grieving their dead children so loudly and so publicly for so long--they have other children to attend to! The pressures may be different, or not, but it's not our place to judge whether they are less.

Finally, as a historian, I'll say: mental illnesses are very culturally conditioned and constructed, and it's sometimes possible to identify, in medieval sources, patterns of symptoms that we today would recognize as similar to what we call a distinct disorder. This can be a dangerous path, though--looking for symptoms from a checklist is an imposition of modern ideas onto a past. It's much more helpful to investigate how medieval people understood the world.

With all that background, there are certain things in the Middle Ages that can seem to overlap with our modern idea of depression. I mean, melancholia goes back to Hippocrates! One particularly medieval example is the sin of acedia or accedia, precursor to "sloth" in the Seven Deadly Sins hierarchy. While sloth typically gets interpreted as laziness today, acedia is more like "listlessness of the spirit". Late antique monk-author John Cassian describes it thus:

He looks about anxiously this way and that, and sighs that none of the brethren come to see him, and often goes in and out of his cell, and frequently gazes up at the sun, as if it was too slow in setting, and so a kind of unreasonable confusion of mind takes possession of him like some foul darkness.

Polymath nun Hildegard of Bingen was sort of the Dear Abby of the 12th century. While she wrote and answered a lot of letters advising and exhorting kings and bishops, she also responded to hundreds from monks and nuns across Europe, struggling to choose a religious direction (frequently, wishing to shun the position of abbess or abbot to which they had been elected for fear of giving in to vanity and the duties distracting them from prayer). She answered lay people worried about whether their dead spouses and, heartbreakingly, children were in heaven, hell or purgatory.

Intriguingly, a whole complex of outward symptoms that we might relate to particular expressions of mental illness became linked to a very female idea of holiness in the late Middle Ages. The extreme food asceticism to the point of starving to death is the most famous (cf. Caroline Walker Bynum, Holy Feast and Holy Fast), but digging into the hagiographies that don't read like straight-up copies of another, you can see the edges of something like acedia: inability to drag themselves out of bed, not bathing, isolating from their monastic sisters even more than their community Rule mandated silence. But if we can take the personal account of Margaretha Ebner as reflecting her mental, not just spiritual, state, even some of those women perceived their experience as beneficial if painful ("suffering" is a common theme, but it's not always clear what exactly that means).

Seriously, if you're interested in this topic, I can't recommend Bynum's book highly enough. She's a genuinely compelling writer, the book has some really good introductory sections for non-specialist readers, and it's a great tool to learn how to deal with a phenomenon historically instead of projecting modernity onto the past.