A lot of Ts will talk about a person's "internal dialogue", which is the constant stream of "thoughts" in our head. When we refer to them as "thoughts", it sometimes confuses the situation and makes it sound like it shouldn't really seem like a 'voice'.
Actually, for a lot of very level-headed people, it's much more like a 'dialogue'. Oftentimes it becomes really chaotic, particularly if you're unsure, emotional or conflicted about something. And for plenty of people, it can become a really crowded, noisy place upstairs sometimes.
I have DID, and since working in therapy and getting to know my parts, we have conversations in my head every day. Sometimes one of my parts will interrupt me in the middle of an activity and it's just plain annoying.
Thing is, that before I started getting to know my parts - I didn't really know they existed at all. They didn't ever talk to me. DID takes an average of 7 years in therapy to diagnose, because it's not obvious or overt - it actually survives by being covert. So it quite often takes work for a person to be able to 'get in touch' with their parts.
The point of that is not to say "You don't have DID". Not at all. If it's concerning you? Raise it with your T.
The point is more to say that DID oftentimes doesn't present as "internal dialogue" - to the contrary, it usually takes a concerted effort to get that dialogue going. And for a lot of people in this world, their head is often a really noisy, chaotic place, and there's nothing to pathologise there at all.
Frankly, I think it's good to have questions, it's good to want to know, to understand. But in this case, what you're experiencing may be fairly consistent with someone who has a lot (like, A LOT) to deal with. It wouldn't be unusual for someone under a lot of pressure, dealing with some really tough things, to have a lot of different conflicting thoughts, and even for some of your own thoughts to be quite distressing (like, phwoar, where did THAT idea come from!). That makes sense to me. So be gentle with yourself, and your head - you're dealing wih a lot of difficult stuff at the moment.
And if you're concerned or have questions about it, do raise it with your T. They are best placed to give you insight into whether there's a dissociative disorder possibly in the mix.