Extremely Leash Reactive 18-Week-Old Mini Aussie Puppy NEED HELP!!

I brought home a Miniature Australian Shepherd puppy at age 14 weeks (thought she was 9-10 weeks because of the birthdate listed online), so when I got her, her socialization window was closing or basically closed. She was really sweet and quiet, but a bit shy. (I wanted the calmest of the litter and the breeder said she's a sweet cuddle girl.)

Day one, immediately when I brought her home, she started opening up to me, and would come up to me for cuddles and pets. I spent a good amount of time with her, fed her, made sure she went potty (pee pad), let her explore my bedroom and kitchen. At this point I knew (or thought) she was a really well behaved puppy.

In terms of socializing her, I went a very aggressive route hoping that her socialization window was still open. So on the first day, I took her to meet a group of people at a nearby friend's house, and she did really great. Even now she does great with all people and is great with kids. She explored and sniffed all around the house and interacted amazingly with everyone, which I took as a good sign.

The next day I decided it was time to take her for a walk (breeder told me she already had 3 rounds of core shots and gave me a set of the used vials to show the vet) she did great until we encountered a dog. She went up to the dog in what I thought was a confident manner, but the moment her nose touched the other dog's nose she, with no better way to put it, screamed very loudly and darted away from the dog, but she couldn't go very far because she was leashed. The other dog stayed very calm the whole time and seemed very confused.

After that incident, I tried my best to have her meet other dogs much more slowly and I was successful with the next two dogs she met. I had them in the same room but not interacting and then slowly allowing them to get closer without touching. Eventually my puppy started initiating play. I think it helped that the other dog was not interested in my puppy at all. After that day, I took her out again, hoping that the positive interaction with the two dogs would help. I had her slowly meet a dog, but again she yelped (not quite as loudly as the first time) and tried to flee, and another dog came up to her and peed very close to her.

After that she started holding ground and barking/growling at other dogs.

I immediately looked on Yelp for trainers and chose to contact two trainers based on location and high number/highly rated reviews. One charged a ridiculously high price for meeting once (3+ hours as needed), and the other took a long time to respond, but I was getting desperate and scheduled a one to one ASAP. They say that they "use only science-based, 100% positive reinforcement training methods endorsed by the AHA, HSUS, SPCA, ASPCA". What I found was really concerning during the session was that when my puppy was reacting, the trainer tried to lure my puppy with treats to get her attention, and although she was barking during the whole process, the trainer kept giving her treats and never corrected her behavior. Right after the session the barking became overly excessive and now she barks, growls, and lunges at what seems to be any ground animal (so far cats and squirrels. I tried the same lure method, but my puppy does not easily follow treats. As of now, whenever she starts to react I try to calmly pick her up and wait until she calms down to start walking with her still in my arms. She's going to get bigger and I won't be able to pick her up like this probably in the next week or two.

She's much better off-leash especially with a lot of people/dogs around, but does still give warning barks and growls at dogs about a street distance away if it's just one dog. Once I go and interact with the dog and she see's that it's harmless she will stop barking, sniff the dog, and either plays with it or ignores it. It also seems like she does this mostly to protect me, since when dogs knock me over, or are constantly jumping on me she rushes over and barks at them.

I really want to be able to go hiking and run with her; this is the main reason why I got her. I'm very cautious to even take her out for potty (she only pees and poops outside and I currently take her out 5 times a day). For exercise I've been taking her to unleashed parks the past several days so she can meet new friendly dogs. She doesn't seem to have much energy because at home she sleeps all day and only engages in play about 5 minutes a day. Although she's been pretty easy to train, she also doesn't seem very excited during training sessions with me even though I use favorite treats and a very genuine upbeat voice. (I love her very much!!)

Some extra info: I think she is a high anxiety/fearful puppy because when I first got her she had bad car sickness (drooling and vomiting according to the breeder), but on the plane ride home she had no signs of drooling or vomiting and she was sleeping the whole 4 hour ride. She drooled on the 30 minute car ride home from the airport. I wanted her to get accustomed to car rides so I held her while someone else drove. After one 5 minute car ride she completely stopped drooling and lip licking.

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