First of all, I am sorry to hear of your situation. Like many, I have been in bad relationships, and I am glad to learn that he has left. I hope for the sake of you and your children that it really is for good.
Secondly, I am an Audiologist. Pain releif and keeping the ear dry are the most crucial immediate care components. Cotton balls are inadequate for keeping the ear dry. The waxy plugs for swimming are better. You can shape them yourself so they don’t go too deep into the ear canal, but to form a seal around the canal opening to block the water. Rubber flange-shaped swimmers plugs might not work well at this point because not everyone has the same shape or size of ear, and if you choose ones that are too small for you, they could go in too deep.
@sandystrachan is incorrect… there are treatments for broken eardrums, but the treatment depends on the extent and location of the rupture.
I have seen people whose eardrum burst from the pressure of a blow to the ear, as well as from pressure changes in car crashes from airbag deployment. They are not as common as accidents with cotton swabs (e.g. Q-Tips) or eardrums that rupture from fluid build-up and infection behind the eardrum.
However, the fact that it was air pressure rather than a foreign object or infection that caused the rupture can be an advantage, because there is less risk of you developing an infection. That is most likely why antibiotic drops were not prescribed.
I can’t guess what is meant when they say the drum broke in half… if it is a clean tear, it may well heal nicely on its own, and there could be minimal lasting impact on your hearing. On the other hand, if there is a hole the size of half the eardrum, surgery may be required to patch it. The extent of lasting hearing loss will depend on how well the perforation heals, how much scar tissue forms, and the location of the perforation/scarring.
Your age is a benefit, since younger people tend to heal better (assuming you have no other health concerns). Of course stress makes any problem worse and impacts how the body’s systems work in healing and fighting disease. So again, I hope that this relationship is truly over, and that you are able to find a safe, supportive environment in which to raise your children.
I wish you the best, and will glad answer any other questions you may have. Take Care.