Here are some psychological and scientific perspectives on the feeling that your characters are writing themselves, and a few bits of advice for writers who write this way.
Bicameral brain theory
The Iliad and The Odyssey begin by invoking the Muse to inspire the storyteller. Other works from in or before that era (everything Older Than Dirt, and some early Older Than Feudalism works) usually also begin by claiming or inviting divine inspiration. Julian Jaynes, in his book The Origin of Consciousness in the Breakdown of the Bicameral Mind, argues that this is because all storytellers and artists in the era experienced writing as something that was channeled through them. He says that people from this era experienced parts of their mind as "gods" who would give them commands that were heard and processed as actual speech. Then he advances the idea that this is also how you explain things like spirit-channeling rituals. (He further posits that all volition and creative problem solving came from these hallucinatory gods, but that's a bit of a stretch.) This is now regarded as a load of dingo's kidneys, but it's been used in some good fiction just the same.
Most people these days don't actually experience their muses - or their characters - as literal voices. But the I Just Write the Thing sort of writer will usually have characters that they can "dialogue" with in some form. And the notion of getting inspiration and having to capture it on the page - isn't that a bit like spirit channeling?
The Muse and the Mun
In some places (Livejournal Roleplay, and probably others), there is a practice of externalizing your characters so as to write messages directly to them, or make them talk/write directly to you. If you are a discovery/seat-of-pants type writer, sitting down and negotiating what they want to do next and what you want to happen next (in a side document that is not part of your writing) can be an effective way of getting the plot back on track if it has been wandering for a while.
Editing
Some people find that throwing the first draft onto the page is mostly done by the muse... but then they are left mostly alone to do the editing process. Do not be discouraged by this.
Muse-writing can be totally irrelevant to the main story. Most muses do not have the best grasp on story structure. So editing can be used to trim the plot into a more manageable shape, by moving the sequence of events around, or removing parts that don't go anywhere. (If you particularly like a bit that is pointless, or your muse refuses to let go, move it to a "scraps bin" file.)
Inner Critic
The inner critic is the Evil Counterpart of the writing-muse. Instead of a metaphorical inner voice that shoves inspiration through your fingers, it is a metaphorical inner voice that actively prevents inspiration from going anywhere. (It also does other not-creativity-related stuff, but that is another topic that is covered elsewhere.)
Psychological classifications
Obligatory disclaimer: TV Tropes should not be used to make a self-diagnosis. If you find this useful enough to want a diagnosis, get outside perspectives - and at least one professional, if your area has any psychologists/psychiatrists - to check your work. Even if you do have relevant education and training, Informed Self-Diagnosis is heavily frowned upon. Requests for advice on the discussion page should not, and will not, be answered.
In general, if you are capable of functioning as a human being in society, and you feel fine about your identity and the relationships between you and your characters, you do not need a label for - and should not be diagnosed with - a psychiatric disorder. But if it becomes too extreme to deal with, here are some pieces of terminology.
Saying that your characters have "voice" might be interpreted by some people as schizophrenia at first glance. If you are still perfectly capable of determining that characters are ultimately still fictional, do not experience any other sorts of hallucinations, and are otherwise capable of carrying out daily life, this is not schizophrenia.
This may also be interpreted by other people as being Dissociative Identity Disorder (DID). This kind of writing is not that, either. Not usually. For a full dissociative identity diagnosis, you must also not remember large parts of your life (significantly worse than normal forgetfulness), and at least two distinct separate frames of consciousness (different "alters", as some people call them) where being in one is capable of making the other(s) "black out"/"lose time".
If one is distressed because writing feels like it is happening without your will or agency, this is a symptom called "depersonalization". If someone experiences this and not any of the other things above, that's depersonalization/derealization disorder (which is sometimes abbreviated to DPD or DPDR).
