I'm ashamed before God. Can I even pray?

Yes, and the shame is not the obstacle you think. There is no threshold of cleanliness you must reach before speaking; if there were, no one would ever speak. Start exactly where you are, including with the sentence: I don't think I have the right to be saying this. That is a prayer. The oldest teaching is that the door is not locked from the inside, and the one who feels furthest is often the one being waited for.

The tradition holds that God will not despise a lev nishbar — a broken heart: the very state you are ashamed of is the one it says is welcome.

From the sources “A broken and contrite heart, O God, You will not despise.” — Psalm 51