is my dog not loyal or not trained?

The problem is you have had a dog for 3 weeks and expect it to be perfectly trained.
Ok- for starters are you aware that there are leash laws and that it is illegal to walk your dog without a leash unless it is in a designated leash free zone.
This is for your dogs own safety- especially when she isn't trained in recall.
If she ever approached someone with another dog that was on leash- and the other dog mauled her, for example- the other dog's owners would not be liable and you would be up for the costs. The same goes if she ran in front of a car, or was hit by a bike, etc.

It sounds like she is very social which is fantastic and definitely not something you want to disourage, but you need to work with her and train her well if you want her to follow your commands 100% of the time- especially in areas where there are loads of distractions like new smells, sounds, people and animals.

you need to train her. you shouldnt let a dog off the leash when it wont return. get a long leash (i use a horses lunge line) and constantly call the dog back and give it a treat. if i call him and he doesnt come, i just tug the leash a bit and he gets his treat when he comes to me

You need to keep her on a leash ALL the time in public. What would you do if she ran towards people that were across the road? She could get killed or cause an accident and Innocent people could be also be killed. If you can't afford a leash then use a washing line or something.

it's because she gets over excited when she see's other people. my staffies the same, he nearly pulls me off my feet when we see someone we know! i've never managed to get him out of it, i hope you have better luck! when you see someone out you should never let the dog pull you over to them, you have to make the decision. wait until she's calmer then YOU walk HER over. Dont let it be the other way round or she will think this is acceptable as she gets exactly what she wants

you need to socialize her more so people aren't a huge deal. walk her on a leash so she gets the point she is meant to stay with you. when she pulls to great people on the leash make her sit and when she does give her a treat. its not a question of loyalty it's just like an excited child