Hi, I'm sorry this is happening to her, that's a weird situation. So she gets the same 2 cuts in the exact same places on her face/head every time she digs in her lay box?
If you could post a few photos of the cuts it would be helpful, as you say they look deep. I can certainly see a beardie getting scrapes and scratches from digging with their face/head first, but I'm not exactly sure how she would get "deep" cuts...What do you put in her lay box? Are there any larger stones, rocks, pieces of wood, etc.? It should just be screen-washed play sand that is just moistened enough that she can dig a tunnel that won't collapse in on her, but not very wet or damp. I've also seen people mix in some plain old topsoil or cocofiber (EcoEarth), but that's it, you don't need to put anything else inside her lay box at all, no rocks, stones, pieces of wood, decor, etc.
It's going to be hard to keep the cuts clean while she's actually digging, but in the meantime you need to go and buy an antiseptic wound cleaner, the best are either Betadine (povidone iodine) or Hibiclens. You can buy both of these at any drugstore or Walmart. Mix them with warm water (I do a 3:1 ratio of warm water to antiseptic; if using Betadine mix it so it ends up looking like weak iced tea). You can use clean, sterile gauze or a very clean washcloth and soak it in the antiseptic mixture, then kind of drip the solution down over and into the cuts, then gently wipe away any sand, dirt, etc. that is in or around the cuts. Normally I tell people to actually soak their beardie in the antiseptic mixture, but because this is on her head and near her nose and eyes you can't submerge her head in the solution. So you're going to have to do your best to wash the cuts out very well with the antiseptic, you can also use sterile cotton swabs if there is any dirt or sand down inside the cuts. Try not to get any of the antiseptic in her eyes or nose, both Betadine and Hibiclens will burn. After you get the cuts all cleaned out with the antiseptic, you should gently pat her completely dry with a very clean washcloth (buying a box of large, sterile gauze pads at the drugstore or Walmart is best to use for wiping/cleaning out the wounds with the antiseptic and patting the cuts dry). After she's dry you need to apply a triple antibiotic ointment to the cuts, like Neosporin or Bacitracin. I'd do this twice a day, the cuts should hopefully scab over fairly quickly.
Hopefully you can get the cuts to heal before she lays again, but if not then you're going to have to clean her wounds out with the antiseptic before putting her into her lay box, but do not apply the antibiotic ointment to her before putting her in the lay box, that will only create a huge mess and get sand and dirt stuck inside the wounds. I don't know what your schedule is like as far as having her in the lay box, but I would clean the wounds out with the antiseptic before putting her in the lay box, dry her well, put her in the lay box for a few hours, and then take her out and clean the wounds out with the antiseptic again, dry her, then apply the antibiotic ointment and let her sleep in her regular enclosure for the night (no loose substrate in her enclosure, only tiles or paper towels, carpet, etc.). Then in the morning wipe the antibiotic ointment off, clean the wounds out with the antiseptic mixture again, dry her, then back in the lay box, etc. and just repeat until she lays all her eggs, then continue the treatment until the wounds scab over.
My only concern is actually how deep her cuts are, because she may end up getting sand, dirt, etc. inside and making the cuts worse with her digging. I have never done this myself, but maybe someone else can chime in about using paper towels, a blanket, newspaper, etc. in her enclosure to allow her to lay her eggs underneath and not actually using a Kay box with dirt or sand at all. I've seen this before, also I've seen Alfalfa pellets used, which would be much cleaner than sand or dirt...
