I studied engineering at university for years then decided (after a lot of struggle, because I did like engineering a great deal too) to do music as a career.
Tell you what, both careers will be tough and difficult, if you choose engineering you have to be prepared to live with the fact that your musical potential will NEVER realise its maximum as it would if you where to devote your life to your muisc. If this fact is unbearable for you then you must do music, if you can live with it then you must do engineering.
If you choose music then you shouldn't expect money to be a big part of your life. If you have desires to earn a living off performance then you should really try to put yourself under pressure music learning wise. You should force yourself to memorise and master faster and faster all the music you get your hands on. Most people have some fantasy that becoming a musician is easy and its just like learning music at the rate you did when you learnt as a youngster with your teacher. It isn't, in fact choosing music as a career demands a huge amount of organisation and self disipline if you want to achieve anything and really music condemns you to a hermits life in front of your instrument.
Choosing music as a career should have nothing to do with money, society or anything else. You choose to do music for your entire life because you have no choice, you are drawn to it, or you must use it to live! I have met many musicians who do it only to live, because otherwise they would be unemployed and on welfare. I think this must be a requirement for most musicians, the music within us distracts us so much that in a job outside of music we will never be fully focused.
If this doesn't sound like you then you shouldn't push aside your engineering. All musicians who devote their life to music as their sole occupation do it because if they didn't they would not be living life. Music is life for a musician, they cannot be seperated from the relationship.
If you are uninterested in teaching music (something 99% of musicians end up doing) then you are simply putting yourself on the MOST risky of all musical occupations. To be only a performer and earn your sole income from concerting is very risky and is destined to fail more often than not early on in your career. The longer you hang in there, the more you build your name, the easier it becomes, but you should expect 20+ years of trying to build your name before it become easy!
Being a performer is a business, it no longer has anything to do with how well you can play pieces, or how much you have practiced. It has everything to do with selling seats and trying to encourage people to return the second time round. The golden secret is to give your audience something they didn't know they needed, do that and you are on your way to a successful performance career.
Businesss is tough and ruthless, trying to sell your concerts is going to be very demoralising if you don't work your ass off. The reality is, YOU must sell practically 90% of the tickets to your first few concerts. If you put posters and talk on radio or get in newspaper articles, this scatter gun approach will only hope to sell you a few tickets here and there, nothing which would really pack the concert hall. So how you go about doing this is all up to you, and this is where most people fail, not because they can't play the piano, but because they have no idea how to market themselves. DO NOT GET A MANAGER TO DO THIS, you must be able to do it all yourself before you even imagine to have a manager. If you do not know the ins and outs of your own business then you are setting yourself up for disaster if you totally rely on someone to do it for you! Learn how to sell seats to your concert, it is very exciting!
I remember giving preview concerts before my first solo recital at the Mandurah Performing Arts Centre at a local Yoga club. This club had about 100 members to which I played relaxation, medatation music for them on the concert Yamaha upright they had in there. At the end of the session I sold there and then 40 odd tickets. Now I also went to retirement villiages, local schools, churches, univeristies and other social clubs. It is all about networking, getting to know the community that you are playing your concerts in. This is how you must do it if you are starting out, the community must get to know you, this can be hard in a big city, but in smaller communities this is a breeze.
I personally find selling tickets to concerts in a town with population of 1000 much easier than a city of millions. Simply bceause you can network yourself easier with less people! Up in far north West Australia they rarely have concerts of any type so if someone turns up willing to entertain the whole town flocks together!
A musicians path is not linear. You might see people making names for themselves with big international concerts, or graduate from famous schools with famous teachers. This is not the only way to go, this is A way, but a musicans life is not this one dimensional. You do not even have to have an international career if it doesnt interest you! You dont even have to perform. You could play piano for yourself for the rest of your life and that would be a musicians life, selfish albeit.