How do I treat this?

TW:descriptions of cuts

So, a week ago I cut pretty deep. Not sure what layer but it was gaping a bit. I'm pretty sure it's infected now. It's still open and is a yellowish color. There is redness around the wound. While I've dealt with infections before I haven't had any this deep. I'm wondering if the course of treatment is different for deeper cuts. All I have right now is an antibacterial cream. (Yes, I know to apply it to the edges and not directly in the wound) I also don't have steri strips or anything like that. Thoughts?