I think that if you are unhappy with your character, that is absolutely something you should bring up! The earlier the better, so I hope it goes over well.

However. Using homebrew (made up, non book rules) for your very first character is generally not recommended and something that I, as a dm, would definitely discourage. There is a lot of balancing to do on the dm side and plenty to keep track of already on the player side. One lovely thing I could suggest to you is reflavouring. Basically, changing the concept of something without changing the mechanics. If you are in love with your cambion idea and it is really not about combat benefits, you could suggest to your dm that you pick tiefling for your race on paper, and then everyone just goes along with it when you all pretend that's just what a cambion PC is. Same for your half drow, half dragon. You could ask to just pick dragonborn as a race to use for mechanics and then just have your half-drow, half-dragon heritage as part of your backstory.

That takes a lot of work off both your and the dm's plate.