Advice for a young person living in a western city

boredom breeds states of unwholesome pleasure

Boredom already is an unwholesome state. It is a form of aversion. It is caused due to paying unwise attention.

However, do you believe there is anything wrong with actually playing an instrument?

One plays or listens to music because of the wanting to please the ears. That is indeed unwholesome. But this does not break any of the five precepts or go against the right livelihood. So playing music for entertainment/money is allowed for a layman.

do you think it is possible to find good employment...

Yes, there are plenty of options for Buddhists. You just need to avoid wrong livelihood. ex: teacher, doctor, mason, engineer, farmer etc.

how can a young person living in a western city separate themselves from pop cultural influences without withdrawing from society

Buddhists need not separate themselves from pop culture. They just need to avoid breaking precepts.

it seems like withdrawing from my life would hurt and confuse more people

If prince Siddhartha thought like that, we wouldn't even have Buddhism today. Trying to satisfy the clinging of others is never a good reason to stay away from the Dhamma. As long as they have clinging, you can't stop them from getting hurt, no matter what you do. But usually it's our own clinging that keeps us in lay life or away from the Dhamma. That clinging can conceal itself as caring for others. Defilements can be very tricky. When you disallow them in their raw form, they try to get in by taking the form of the things you allow.

since there is not even a temple here it is hard for me to accept Buddhism itself as a religion in the strict sense

You don't need a temple to be a Buddhist. You just need to take refuge(spiritual) in the Triple Gem. You can do it privately. There are lot of free Dhamma books/videos available online. If you can't meet a monk face to face, there's a community of online Sangha.

The most hard-core interpretations of the suttas would probably make anyone feel as though their chosen career doesn't jive with Buddhist doctrine. Fortunately we're all encouraged to take a middle-way approach in all things, so we needn't be tied to the strictest way of thinking about our careers.

Right livelihood, the fifth element on the Noble Eightfold Path, is actually fairly easy to summarize:

Right livelihood means that practitioners ought not to engage in trades or occupations which, either directly or indirectly, result in harm for other living beings. (Source)

I think a musician would need to go out of their way to harm other living beings. The career is inherently peaceful in nature, and does a lot of good. Buddhism isn't about avoiding all sense pleasure and completely eschewing anything "fun"; it's more about following a middle way that makes sense for the practitioner.

On a personal level, I have a profound appreciation for musicians. Music helps me relax, and I really enjoy opportunities to listen mindfully. Back when my children were babies, there were some nights when being able to tune into the classical radio station meant the difference between complete peace and total discord within the household. Music does wonders for people, and musicians make it possible for people to benefit from it.

So, music as a career: no problem. Go for it, and don't look back. Your other concern, about economics driven by consumption, could have an entire book written in response. But, simply put, there is nothing wrong with providing a service and charging a fair price for it. This basic practice of trade transcends all modern economic theory, all "-isms", and all other ways of thinking about money, goods, and services. Charging money for the consumption of music is no different than charging money for the preparation of food; both are perfectly valid ways to make a living in the world. Both provide something of value to a consumer. It's all good.

Finally, you needn't withdraw completely from life to be a good practicing Buddhist. Again, it's easy to get caught up in the strict interpretations of precepts and rules, and to let that push us into thinking that the only way to live the "right" kind of life is to put on robes and meditate all day, but it's important to unwind a bit and always remember the Middle Way. You also don't need access to a temple, a Dharma center, or anything else. You can simply read Buddha's words and apply them to your life; you can accept the Four Noble Truths; you can follow the Noble Eightfold Path. You can do all of this within the context of your current life, being who you are, with school, work, friends, and family. If you would change your life in any radical way in the pursuit of Buddhism, and if such changes would result in suffering for you, then what would be the point? The principal teaching of Buddhism is suffering and its elimination; no one's practice should ever cause suffering.