I think you shot yourself in the foot by lying that you cheated when you didnt... Its hard to build trust when serious lies have happened .

My advice is get yourself together work on your depression and feeling better. Allow your gf time to consider her options. You also need time to think of your options.

Continue to see your daughter... Just be pleasant to your gf but dont try to discuss your relationship and the problems. You both need time to process it all.

Good luck