Try this thread and see if it sounds anything like your hen. It also has a link to another good thread in it. If she is egg bound the Prep H isn't going to help but lubricate like KY or even mineral, or vegetable oil might. See if there is anything in those threads that sound familiar. https://www.backyardchickens.com/forum/viewtopic.php?id=59309
I just had a problem with a prolapse. In the worst case possible, she pushed the egg through the wall of the duct into her abdomin (sp?). We had to put her down, as she was not going to recover. Very sad. Do whatever you can to prevent this. See the forum under .very severe prolapse oviduct for the others advice....Sorry for you, Kellie
Please - what is this hen's diet? And does she have a constant supply of calcium available (e.g. oyster shell)?
The above posts are correct - if she doesn't get good help soon, she will likely die a painful death. As noted above, there are common household items that could help lubricate (mineral oil, vegetable oil). If none of those are in the house, please get them somehow - from a neighbor or whatever. It is troubling if the only folks who drive in your household are not willing to get a being in pain and distress what it needs; it is truly unfortunate that you are alone in this.
It has been recommended in other threads on BYC that in an emergency a Tums be given to help provide the calcium needed to get the egg out (assuming that's the problem here).
JJ
Edited to add that I am wondering if some aspirin in her water (FIVE 325 mg aspirins [NO SUBSTUTUES] crushed per gallon of water) might relieve enough pain to help her get the egg out, if indeed that is the problem. I would like it if someone else weighed in on this first.
lubricate the area (and a bit around the "inside" rim of the vent) with preferably KYjelly (ask your parents) or failing that some baby oil (mineral oil)... repeat the warm bath procedure and relubricate after.
This often happens with young pullets and your photos do not show a severe prolapse so IMHO putting a bird down a this stage is a bit much.
Please do not insert finger and feel around anymore.
If you have a tum crush that and addit to a wee bit of cooked oatmeal (make a couple pellets with it and give to bird) ... this is an emergency substitute for the calcium gluconate given at the vets for eggbound situations.
Be calm and patient and keep your bird in a quiet dark place until she can pass the egg. Once the egg has passed the prolapse MIGHT be "worse" ... this is when you should use prep H or witchhazel (ask your mom if she has that )