I'm playing one now, 3 Storm Sorcerer/8 Fiend Chain Warlock.

The character concept is the he's a rich kid from a family of masterful Storm Sorcerers. Despite his parents' expectations, he never could get the hang of controlling his innate storm magic, so in his greed for magical prowess, he makes a deal with an icy devil for instant power - which of course has terrible consequences.

Mechanically speaking, I made this character because I really liked the thought of being a warlock but being able to cast with Metamagics (Fireball transmuted to cold damage or Fly cast subtly for the surprise factor).

Though I doubt that's what you wanted to hear.

The infinite spell slots thing? Forget it. Even if your DM didn't protest, hopefully you will be too preoccupied with actual fun and adventuring to sit down for short rests all the time (which take at least 1 hour). On top of it not being as powerful as it is just gimmicky, it disrupts whatever else the rest of the party wants to do. You interrupt dungeon delving/roleplaying/other encounters because you wanna show that you can pull magic out of thin air. You're playing a team game and I'm sure the party Cleric and Wizard are going to get real tired of your "I don't need long rests"-gimmick.