It is so hard when you are coping with loss and also have to cope with insensitive people at the same time. My last family dog (before I moved out and got dogs of my own) was put down at 6 years old due to lunging at a neighbours child and almost biting her, she had also previously bitten two adults that were visiting. After having dog trainers out with no success my mum made the awful decision to have her PTS as rehoming her seemed too unfair and unsafe, she loved my mum to death and would have been miserable in a new home. I went with my mum to the vets and was devastated, the next day a friend called to commiserate and asked when we were getting a new dog. That was over 10 years ago and I still have a photo of her next to my bed. I never really kept up with that friend either after that, I just couldnt believe he could have asked me that the day after and not thought it to be insensitive. Surround yourself in people that understand or just chat to people on here if need be. You can never replace an animal, my current dog is the same breed and colour as the last dog. I brought him because he reminded me of her and quite likely from the same breeder (we found out later that her dogs are seriously inbred and have a lot of behaviourial issues) but since he was at a shelter to be rehomed and not through behaviourial problems I got him. Looking at him now I can't see any resemblance to my old dog and am so glad I brought him even though at the time it felt like it was for the wrong reasons. Luckily even though he is quite neurotic (seems to be a bit of a cocker spaniel trait!) he has no aggression and is my little love bug.
It will get easily slowly, just allow yourself the time to grieve and never let someone make you feel bad because it is 'just an animal'.
Sending hugs from New Zealand.