I'd recommend an actual veterinary behaviourist vs this, sounds like its a vet who has done some behaviour courses and thats not the same thing.
Unfortunately anyone can call themselves a behaviourist (I don't I call myself a behaviour consultant!)... which is frustrating when trying to get folk to the right people.
If you possibly can, I'd highly recommend Amber Batson (who IS a veterinary behaviourist, I think she's based in Somerset and is likely to be your nearest, she is Understand Animals on facebook or you can find her by googling.
If you were my client... I would have you put up frosted window film on any window that gives her a view that triggers barking, it only needs to go up high enough to block her view, so not necessarily the full window. I would also remove letterbox, and put a mail box up where she can't see the postman coming.
That immediately removes daily stress, and the better you can lower stress, the better you can teach new behaviours and eradicate unwanted behaviours.
Then I'd be speaking to the vet about anti anxiety drugs, zylkene CAN work wonders but I find either its brilliant or it does bugger all theres really no in between.
THEN.. the actual barking.
For sounds I would chuck a high value treat at her any time she hears a noise, whether you heard it or not.... before you say 'that's rewarding the barking and she will do it on purpose to get the treat'.... Yes, she might BUT.. the barking will go from 'startled, worried' to 'intentional, relaxed' and at that point IF she has cottoned on.. you can then retrain so she has to earn the treat and earning it gets less predictable.
So initially sound = treat, woohoo.
Then later on sound/bark = maybe do a sit, get a treat.
Later still, sound/bark = maybe do a sit, down, spin, get a treat, maybe just get a free treat...
Built it up so it becomes less and less predictable and the treat value and type varies as well, and the proximity of the treat also varies (so initially youd have treats in your pockets... by the end youll MAYBE have a treat in your pocket, maybe you go get one from somewhere else).
SO first you change the emotion... THEN you can refine behaviour to what you want, once its no longer driven by just emotion.
The 'being near you' this is what tells me your dog is still anxious, all my dogs love to be near me, but they can all also sod off when told. When they NEED to be sat in my lap, I know something's worrying them!
I would teach her some useful cues here, off, on your mat, back up, wait... all of this requires a dog who has some ability to tolerate frustration and right now I don't think she does.
Finally, look at her typical day, write it down in bullet points. Score each item + or - for whether this activity/event adds stress or removes it. Remember that even things she finds fun, can still be adding stress.
It may be there are some simple tweaks you can add to your daily routine that either avoid stress, or give her an outlet for it so she 'warms down' after something super highly arousing.
For example, a walk with lots going on, play with a toy, greeting another dog - great fun but, that's definitely a + in the stress bucket.
So finish a walk by scattering food in the garden for her to sniff out with her nose and maybe licking something off a Lickimat... thats enjoyable but should empty some out of the stress bucket.
I'd also caution to have realistic expectations... shes a pug, she likes to bark and she likes to snuggle and she's not going to suddenly one day NOT be a pug... but I do think she can be more chilled and less irritating to live with than she currently is!