Alright let's get through the nitty gritty of this shall we!
First dialogue encounter
You're still sleeping? You promised we'd meet for breakfast.
- That line seems fine enough to me as it establishes as though nothing has really happened
I'm sorry...I...I just had a terrible nightmare. I dreamt you were dead.
- The idea behind the line is solid but the execution could probably be slightly changed, maybe something like "Huh what? Oh, I'm sorry...It's just that I had this terrible nightmare. I dreamt that you were dead..." Just to establish that Thomas is still composing himself after waking up from a terrible nightmare but then realising he's been asked a question snaps back into being composed but still shaken up.
That's silly. I'm fine. Besides, you always promised you'd take care of your little sister.
- Similar to the line before, good line but needs a little tweaking. Depending on how you want Gabby to be presented, if you want her to come across as quite innocent and charming then you could be like "Hehe that's silly. I'm fine Thomas. Besides you always promised that you'd take care of me." Just to add a bit of delight to her with a little giggle, also removing that sister bit as it comes across as a little exposition-y
That was when we were kids
- Nice line to show that he's reminiscing of the good times they had but also a little dismissive of her. Whether that be because he's not one to boast that he could protect her or maybe that he's just afraid that he can't protect her so he's trying to ground her by reminding her that he made that promise when they he was less rational and more immature, could go either way though so! But if you want to emphasis the bond that they both have together you could add like a little chuckle at the beginning just to establish that now that he sees her and is talking to her, especially after dreaming she was dead, he feels comfortable with her and relieved that she is actually OK. Just a suggestion though
It's still true, isn't it?
Nice follow up, showing Gabby's fear that Thomas doubts himself and wouldn't protect her.
Yeah...
Further emphasising the fear that he can't protect her with just a deflated "Yeah...", nice
You look tired. I'll wait outside so you can get some sleep
I feel like there's some dialogue that's either missing before or after this line, I'm not quite sure though why I feel this way. Maybe it's just me

hahaha
I would pitch some new dialogue here but it's hard to do that without knowing the entire story so it probably wouldn't be very effective in the context of the entire game hahaa. Maybe something like this though perhaps:
"You look tired. I'll wait outside so you can get some sleep"
"Gabby please, I just dreamt you were dead...Could you please stay, even if it's for just a few minutes?"
"Oh don't be silly, you'll be fine once you've had some more sleep. You always loved your sleep when we were younger hehe" --Gabby proceeds to leave--- "Sweet dreams..." Then get up out of bed.
(I don't proclaim that I'm the best writer but I thought I could have a stab at it hahaha

)
Second dialogue encounter
Gabby, wh...what's going on?
Good question Thomas hahaha
Please address me as Doctor Smith
I feel like she wouldn't say this if he's been at the psychiatrist for a while now, maybe something like "Now Thomas I've told you before, please address me as Doctor Smith". Just to imply that he's been there a while and it makes more sense that way.
But you're my sister!
I'm not sure about this line, I feel like stating outright that he's her sister seems a little on the nose but I get what the line is intended to achieve. Maybe you could change it to like "W-w-where am I?" as it makes sense that he's only just realised that he's in a completely different location to before (Just as another option though, you can keep the sister line if you like hahaa)
No I'm your doctor, and you're in a mental asylum
First part of the line is fine but the second half seems a little exposition-y. Perhaps you could change it to like "No I'm your doctor. You should know this, you have been here for quite some time" or going off the line I suggested earlier "You've been here for quite some time Thomas, you should know where you are."
Wh...why am I here?
Perfectly fine line I feel
Why do you think you're here?
Loved this line, perfectly vague and suspicious as to what's really going on. Alluding that this version of Gabby that Thomas is talking to now knows more than their letting on, great stuff
I don't know...
Good line although maybe to make it follow smoothly into the next line you could add like "I don't know...I just-" then get cut off by Gabby saying the next line
You've reached the end of your session. Please see yourself out.
I like the bluntness of this line, as if she doesn't care really.
Whew that was a lot to go through, I hope that some of it was useful hahaha
Again I don't proclaim that what I suggest is the best thing to do but I just thought I'd add my two cents into the topic on how I felt about the dialogue. Who knows maybe it'll help in the long term! Hahaha
So yeah the dialogue is mostly fine at the moment could just do with some minor tweaking I feel
