Do reactions carried out in light always follow free radical mechanisms?
Often, yes; but sometimes not, and generalisations like that often don't work in organic chemistry.
It's a better idea to understand why there's a correlation between &quot;light&quot; and &quot;radical reactions&quot;. One way of generating radicals is by breaking bonds, and one way of breaking bonds is to use light. Of course, this only really works for relatively weak bonds, such as the Br–Br bond, or basically any kind of bond between Group 16 and/or Group 17 elements (O–O, N–Cl, ...). Many of the classic radical reactions involve this kind of pattern, and this is probably why you're drawing this link.* Examples include: free-radical halogenation, the Hofmann–Löffler–Freytag reaction, and the Barton reaction.
Alternatively, if there aren't any weak bonds to break, it could be that you're trying to use light to promote an electron to an excited state. Now, because the vast majority of organic chemicals are closed-shell molecules (all electrons are paired), when you excite something you're going to get a radical species. A simple example is the Norrish type II reaction. This radical generation can be indirect as well, occurring via excitation of a photocatalyst, which then oxidises / reduces an organic substrate to form an organic radical. This is the idea behind photoredox catalysis, which has been a very, very hot topic in recent years.
It is not wise to make a sweeping generalisation, though. You could excite a molecule and have it react immediately, without generating an intermediate radical species. This is the case in photochemical electrocyclic reactions, for example. And there are many photoisomerisations which (as far as I am aware) occur in a single step, without going through a true radical pathway. A very important one is the cis-trans photoisomerisation of retinal. The mechanisms of these reactions are not well-described by the curly arrows of organic chemistry: you'd need to learn some photochemistry to get a good idea of how these work.
And not every chemical relevant to organic chemistry is closed-shell. Dioxygen, O2, is a diradical species; and when you excite it, you get an excited state where the electrons are paired up, usually referred to as singlet oxygen.† Singlet oxygen reacts with other organic molecules in a decidedly non-radical fashion: for example, it does classic Diels–Alder reactions and ene reactions.

* Note that many of these can be also accomplished by simple heating, which can break weak bonds too.
† Usually dioxygen is not excited directly. A photosensitiser like rose bengal is used.