Wow! You asked this 10 hours ago and no one has answered?
Okay. I’ll lead with the chin. Yes. In fact we are told to bring our anxieties, our concerns (and is that not a good description of our complaints?) TO GOD.
Personally speaking, do I sometimes complain to God? Well, actually, I do it so much, I have started praying that God would help me to stop grumbling about everything! To be grateful, instead. And actually, gratitude does much more for me than grumbling.
As to actual complaints: I have to bring them to God IF they are not things I need to bring to the attention of a brother or sister in Christ first.
See Matthew 5:24 New International Version (NIV)
24 leave your gift there in front of the altar. First go and be reconciled to them; then come and offer your gift.
and read around that. All of Matthew 5 & 6.