In Pathfinder, I created a level 10 bard, and I want to be my own rock band outside battle. My bard already have a huge performance in singing and playing numerous instruments.

I took Ghost Sound to emulate music and Silent Image to emulate drummers and other specials effects. My DM said Ghost sound can't emulate music precisely.

What spell would I need to be able to play a song like "Warriors of the World" at a loud volume and precisely using the rules as written?

There are a few spells that can do this

There a multiple ways you could achieve this, some will work better than others depending on the exact effect you are going for. Some will require more flexibility from the DM than others. Hopefully you can find a way to make them work.

I have limited my search to illusion spells that are on the Bard spell list, I was also judging most options based on name alone. Therefore, there are likely a lot more ways then I have listed here but this should be a good start.

Major Image could be the best option

The Major Image spell overcomes the sound limitations of Silent Image and Minor Image. You have complete control over the illusion. So you can create a realistic sounding band with a duration equal to your concentration + 3 rounds.

Exquisite Accompaniment is a good option

The Exquisite Accompaniment spell does exactly what you are looking for. It states:

You create a phatom instrument, a glowing construct of magic in the form of a portable musical instrument of your choice. [...] The instrument plays as you direct [...]

Unfortunately its duration is only 1 round/level so you will need to find a way to extend it. The Extend Spell (Metamagic) feat will help you there.

Sculpt Sound is also good

The Sculpt Sound spell states:

You can change the sounds that creatures of objects make. You can create sounds where none exist, deaden sounds, or transform sounds into other sounds. All affect creatures or objects must be transmuted in the same way.

The positives for this spell is that is targets multiple creatures/objects and has a duration of 1 hour/level. You could quickly fill out your band with talentless fighters and make them sound like virtuosos with this spell. The downside is that all targets are under the same effect, so you can only creature one type of instrument with this.

Virtuoso Performance makes you a one-man band

This 4th level spell allows you to maintain two bardic performances simultaneously. Think of a magical looping pedal or mixing board. For 1 round/level you can play two parts in your band.

Shadowbard is a good understudy

Unfortunately this one is a 5th level spell and you won't have access to it for a while. However it says:

You conjure up a quasi-real phantom singer that is visible as a shifting, shadowy duplicate of yourself. [...] When a shadowbard comes into being, it immediately begins a bardic performance of your choice. [...]

Similar to some of the other options, the duration is only 1 round/level. However it will help the cool factor of your band. Additional if you haven't got a name yet, "Quasi-real Phantom Singer" is a sick band name.

Why Ghost Sound doesn't work

In the paizo FAQ there is a question about Ghost Sound:

Ghost Sound: Can this create intelligible speech?

Making something that sounds like speech, and actually making intelligible speech are two different things. Ghost Sound can sound like people talking, but anyone listening can't make out what the "people" are saying. After all, it is a cantrip, and shouldn't be as good as ventriloquism (which is a higher-level spell)

I imagine this FAQ is the source of your DM's ruling. Which is a completely valid ruling and one I would likely make at my table. Also note that ventriloquism won't solve your problem as it only allows you to throw your voice not create additional noises.