Contact mic, flute pickup or condenser lavalier?

[Pandablergs]

Hi, this is my first post.

I've been playing for about 20 years now and recording for about 10. I play in an experimental rock band and on our album we're currently recording, we're leaning pretty hard into using flute on a lot of songs.

Until now I've only been playing c flute, which sounds pretty good live played directly into the dynamic mic I also use for vocals. This has worked pretty well for years though I always dreamed of getting a microphone system for shows.

So last month I decided to pull the trigger and bought an alto flute... which sounds great recorded but isn't working so great played live through my vocal mic. I need a microphone system to get it sounding nice and tasty and deep and haunting on stage. I've been looking into mic systems and I saw a beautiful wireless lavalier condenser mic system, but I was curious, won't this pick up all the guitar and bass coming through the amplifiers? Is this system intended for orchestral soloists?

I also saw a flute pickup system, which I believe is inserted inside the body of the flute. Would this be a better option?

Finally, I saw contact mic systems which range from 20 to 150 bucks, but I'm not too interested in these since my bandmate had a very cheap contact mic to DI system for his concertina and the damn thing never worked very well and cheapened the sound. I know it might be different for flute, but if this is the right option for me, I might need some clear explanation as to why.

What are your opinions? I know im probably in uncharted territory here but any advice would be very welcome. Thanks!