My new pup was like this, he's a rescue and had a very bad start. To begin with I literally couldn't take a step away from him, but we've gradually built it up over the past few months to the point where he doesn't follow me around anymore, but still doesn't like it if I go upstairs without him (dogs aren't allowed upstairs in our house). He is very vocal and after just over four months I can still only leave him at home for 40-50 minutes maximum and that's if he's left with a green feeder full of kibble and a couple of frozen kongs. The minute he's finished his food he starts yelling.
I would recommend trying to build up the amount of time she separate from you when you're home to begin with. Start by just standing the other side of the dog gate from her and rewarding her for not reacting. Do LOTS and LOTS of repetitions until she's almost bored of it, then, when she's used to that and totally comfortable with it, start trying to take a step away, then back quickly and reward if she's calm and quiet. Gradually build up the number of steps and length of time you are away from her, until she's totally happy with you being separate from her, but in sight - and only then try stepping out of sight and straight back in again. I used a clicker to mark the desirable calm/quiet behaviour, but I know some people don't as they think it makes the dog to expectant/attentive.
Once you've reached the point where you can be out of sight for a minute or two you can try giving her something like a loosely stuffed kong or chew to keep her occupied while you try extending how long she's happy for. If you do this enough times she will, hopefully, start to become counter-conditioned and begin to associate your departures with something positive and find it more rewarding to stay where she is, rather than follow you everywhere.
As you can see, there's no quick fix, it takes time and a lot of effort but it can be done. My boy used to literally scream the house down if I left the room, but now - at 7 months - he takes himself off to his crate in another room to sleep and if he's in the room with me he doesn't really bat an eyelid unless he hears the living room/hall door open and then he does get up and whinge a bit, but it's not loud and he shuts up pretty quickly.
My next plan is to desensitise him to the sound of the living room door. I had hoped having all the dcs constantly in and out of it over the holidays might have helped, but I must have a distinctive way of opening and closing it, as he always knows when it's me, even if he's in another room.
We live in a semi and I have pretty much been trapped at home, other than school runs, since August for fear of falling out with my neighbours. Oddly he's ok if we have to leave him in the car - but I don't drive, so that's not an option during the week and I don't really like leaving dogs in cars, even in winter. He is getting better, partly due to the ongoing training, partly as he matures, but it's not been easy and I have had a serious case of cabin-fever at times. I love him to pieces, wouldn't be without him for the world and will never give up on him, but it's hard not to feel some resentment towards him at times - even though I know it's not his fault.
Finally, I would recommend going to training classes with her. It really helps to build their confidence and you develop a different sort of bond, where the dog starts to develop and employ a certain degree of self-control and offer you the behaviours you want in order to reap the greatest rewards - be that treats, toys or your time and attention. She is still very young, especially for a Lab and whilst training is by far the best way for her to learn some impulse control, which will spill over into every day life, some of it will also come with maturity.