Aggressive Pomeranian puppy

Hi all, I really need some advice on my 14/15 week old Pomeranian puppy! Mainly about aggression but a few other things too. So to start off, I recently got a Pomeranian puppy from a registered breeder that also does showing. She’s a very nice lady and really cares for her pomeranians so I think this rules out that as the cause of the issue. My Pomeranian pup when we take her in public, the first time we took her out on leash without me holding her, was 3 days into owning her, at a cafe. when I put her down she started lunging, growling and barking aggressively at everyone who would walk past. Not people coming up to her, literally just walking past a good 5 meters away. We took her to the vets recently and she also did the same thing. When holding her she is fine with people who are super gentle and respectful but will growl at people who are to much in her face, which is fine I think but not sure about the lunging and growling at people and kids innocently walking past.. when I say a firm “no” to not just this, but everything it just makes it worst. I wonder if this is because she thinks I’m joining in with her or if she’s just being stubborn. She is such a sweet dog to me and my mum(who she lives with) but is very off strangers. We got her at 13 weeks old and within the first 3 days we found out she was a bit off strangers so i don’t think it’s anything in my control the cause.. I’m not sure if this is her being scared, protective or just purely aggression. She’s fine with loud noises but I’ve noticed she gets scared of random stuff, like our cats plastic sheet thingo that we use for the cats food she is terrified of it, and also gets unsure with new food and water bowls... but the thing is if she was really, really scared you would think she wouldn’t be attempting to run TOWARDS her fear like when in public when she tries to lunge at people?? I think it’s partly fear and partly aggression. It just came as a bit of a shock because she is so young still and from my understanding pomeranians loved everyone. She is fine with our cats but when one hisses at her she will growl back and try lunge at them through her play pen. She also gets super scared about getting left alone in my room in her crate, I will literally leave to do something and she’ll start crying, is this still normal for this age? Or is she getting seperation Anxiety? I also tried taking her for a walk and it was a disaster, she would run so fast and then flip, or she would insist on smelling and eating everything in sight and no matter how much I’d try call her and get her to keep walking she wouldn’t, so how do I train her to walk on a lead? She is very hyper and friendly, until she’s in public, it’s like two different pups! She is so social and loving I would have never expected her to behave this way which is why it came as such a shock. She also DIDNT act this way towards us when we picked her up from the breeder, which makes me think it could be her being protective of us? Has anyone else had this issue? any advice + tips would be much appreciated. Thanks in advance ?