I wouldn't go to a doctor or a psychologist if you're wondering if you're developing a stutter. They know next to nothing about stuttering. You should see a speech language pathologist who has experience with stuttering to get a good evaluation and determine if you do indeed have onset stuttering or not. It's pretty rare to develop stuttering outside of your teens, but not unheard of. Even if you think it's neurogenic, i'd get a professional opinion. You cant really develop a stutter from most stress or anxiety, otherwise half the world would be stuttering. The only advice I can say is, don't blow it up into a bigger deal than it needs to be. Everyone stutters sometimes, even great speakers. No one is 100% fluent. Not the president, not your favorite actor. So if you're talking and you bobble up with some disfluencies, hey- No big deal. But that doesn't necessarily mean ignore it. If you're worried about it, an SLP is who you want to see as they are the experts. Just make sure they have experience in stuttering because many actually do not and have no clue.