Hello,
Right first things first
You could go round to neighbours with a pack of choccies to apologise about the barking and let them know you are working on it and to bear with you.

It sounds like your pup could be developing Separation Anxiety but as he is only 15 weeks old you've got the advantage that he is young and therefore should be easier to "train" out of it.

Many people have already advised a crate and I agree. One thing to bear in mind though is if you did get one, it's not as simple as getting it and then sticking pup in it when you go out. When you are at home with your pup you need to make lots of positive associations with the crate as a good, safe place to go for a rest or whatever. Best way to do this is to get yourself some puppy kongs (or regular ones)- you may already have these.
Fill up your kong with lots on nice yummy stuff (peanut butter, cream cheese, nature diet puppy food, wet food, wet food with biscuits mixed in etc...). Then encourage the pup to go in his crate and eat his kong in there.
Continue doing this every day or every few days and your puppy will see the crate as a really positive place to go and plus somewhere where he settles down. Also encourage your pup to sleep in there at night.
The next stage is building up the amount of time that he is left. Leave him in his crate with a stuffed kong and walk out of the house for 5/10 minutes. Only go back in when he is not barking. Gradually build up this time period over weeks and months until he is happy being left for a few hours without getting distressed and barking.

Here is a link to a crate training video you might find helpful:
Crate Training a Puppy or Dog Video

Hope this helps

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