Why is my puppy so aggressive?

It’s coming up to a month since we picked up a bichon frise/maltese mix puppy. Things have been up and down, crate tolerance has improved and potty is relatively okay…. But I just don’t know what to do about his behaviour.

Main two issues are growling, biting and then maniac behaviour.

He growls a lot. If we’re outside but it’s time to go back in, he growls and barks and sometimes bites when I try pick him up. He growls and bites the moment we get inside and will not let anyone dry his paws or take off the harness. Sometimes he will be playing calmly and then suddenly start barking, jumping and trying to bite me and my partner. Sometimes he comes up to us to get on the sofa but bites if we try pick him up. He’s very barking and demanding if he sees us eat and wants a treat immediately and will bark if doesn’t receive one.

Tried redirection with toys and sometimes it works and sometimes he gets even more manic. Tried to do timeout but often he will persist chasing after us, biting and other than physically shove him off, there is no way of getting him to stop biting. And I don’t want to shove him off. I’ve been training him commands and he can do sit and down and sometimes touch, but whilst he will do whatever I ask of him to get the treat, he then immediately continues his behaviour. If it’s just me I try to ignore him, but my partner really struggles with the barking and what he’s been happening lately is that we lure him with a treat towards us and then pick him up and throw him in his playpen/crate. He calms down immediately there and starts to cry to be let out… which we do after a few minutes until he stops crying. Often he will just continue being manic the moment he is let out.

I don’t know if this is a normal behaviour that will improve with time and we should just carry on ignoring him and training him commands. Or is this a serious problem that requires a 1:1 trainer? We have puppy classes starting in November, but that is of course a group environment.

I love my puppy. I look forward to seeing him after a day of work and I like the morning kisses and cuddles he gives. But he is such a jerk and I really don’t like him. I cry at least weekly because of him. The relationship with my partner is strained. I don’t know if we are just shit dog parents or I picked up the wrong pup or maybe this is just normal and will eventually pass.