Every puppy is different so I don't think it's helpful to compare yourself to others.
Also I find the definition of toilet trained for some people just means that they recognise the signs so they take them out rather than in my eyes a toilet trained dog is one that will hold it (within reason) and ask to go out every single time.
If you read some internet articles then you would think you have failed if you haven't toilet trained them in 1 week when the more realistic ones say really a dog won't be 'fully' toilet trained (asks to go out every single time rather than people letting them out) before around 6 months of age.
Your puppy is still very very small. Think of every opportunity to pee and poo outside an oppprtunity to reinforce where you want them to go. Whilst every accident is a missed opportunity. You want to sway the balance for the former.
Take the puppy out after it wakes, after feeds, drinks, play and frequently (say every 30 mins) in between. Stay out with your puppy and praise praise praise (if the neighbours don't think you have lost your mind you aren't praising enough
). Use a key word when they go so when you use it again they will start to understand you want them to toilet.
If you find they pee or poo after coming inside stay out next time for longer (I have stood outside for an hour before).
Are you feeding at set times? Keep a note of when they poo as they will get into a routine which will give you a clue on when to take them out and stay out.
If you spot them mid pee or poo pick them up and run outside and then praise like mad when they finish.
Don't be hard on yourself. If you look at the puppy survival threads on here you will find that lots of puppies take many weeks/months to be toilet trained.