Typically, this is why you have to sign a release to hunt on others land, and why you must purchase insurance to have a hunting club, etc.. The owner of the property can be held liable. Not sure if you mentioned who owns the land, which is the entity typically held responsible. Anyhow, no matter what, this is an ugly lawsuit in the making. Plus, you may spend way more than you can realistically get back....
In all honesty, your medical costs should be covered by your health insurance. If you do not have health insurance, but you spend thousands on hunting, leases, hunting accessories, hunting dogs and other items, etc.,.. well, you just learned a very valuable lesson......
You can ask for monetary help, and you can sue if you think you should and want to open that can of worms.... But the best thing is to adapt to the current situation, get on with life, and even possibly get back to hunting soon, with your dog.