I was offered 3 months for free on Apple Music but I was only granted one month

Are you sure, that this email has been sent by Apple?

Identify legitimate emails from the App Store or iTunes Store - Apple Support

There are 3rd party resellers, that have such offers, for example:

...

...

copied from: Free Apple Music for up to 4 months-Best Buy

Maybe you should contact the official Apple Music Support by using this link and ask them, if this offer has been made by Apple:

Contact Apple Music Support

If you are a new subscriber, you can get one month for free:

Apple Music - Apple

You can get more months for free, if you buy or bought an eligible device:

Six Month Offer Devices - Apple