Well, as you didn't mention where said desert was, I'll cover a couple of species.
Crotalus atrox (Western Diamondback) venom is highly necrotic (causing massive tissue damage). It has agents that inhibit clotting, so you get a lot of bleeding and swelling. Many doctors perform a fasciotomy as part of treatment, which is essentially slicing open the swollen limb to allow circulation, as the swelling can be so profuse that it compresses the blood vessels. Opening the limb takes the pressure off the vessels and allows blood flow.
The initial bite burns terribly from most accounts. The choices are a tourniquet which, while preventing the spread of the toxin, will localize and concentrate the damage. On a leg this could mean possible loss of some use of your leg versus total amputation of the foot. Localizing the damage usually means that smaller area suffers far more concentrated damage.
Crotalus scutulatus (Mojave Rattlesnake) is an entirely different bite. The bite is usually devoid of the usual pain, swelling, and bleeding, although some do have a hemorrhagic component. Often a Mojave bite could be mistaken for a “dry” bite where you get punctures, but no envenomation. Presuming the bite of a Mojave was “dry” based on localized reaction can be a dire mistake.
The major components of Mojave venom are neurotoxic. Difficulty keeping the eyelids open, blindness, tingling lips and tongue, paralysis, and difficulty breathing can begin to manifest shortly after the bite. Total paralysis of the diaphragm and heart can follow. If you are SURE it was a Mojave a tourniquet is a good idea in this case, as it prevents the neurotoxins from reaching the heart and diaphragm as quickly.
As far as antivenin and allergies, I’m not sure where you got your information about eggs and fruit, but (as far as I know) groceries play NO part in the manufacture of antivenin.
Antivenin is simply antibodies…just like YOUR body produces to fight off any other invader in your blood such is a virus or infection. They produce this by introducing the venom into an animal that has a strong natural resistance to snake venom. The animals that are regularly used are cows, sheep, horses, and goats. The animal’s system reacts by producing antibodies to target that venom. Some of their blood is then harvested and the antibodies separated. This is then bottled (often freeze-dried first) and shipped to hospitals or antivenin reserve centers. When a person is treated for envenomation these antibodies are introduced into the patient’s bloodstream, and they attack the molecules of venom and break them down.
While antivenin is very successful in doing so, the greatest risk is allergic reaction to the foreign antibodies. Anaphylactic shock is a possibility. The most extreme cases can result in cardiac arrest. Patients are monitored and, at the first indications of allergic reaction, large does of Benadryl usually follow.
For those who keep venomous reptiles in their collections, as well as those who work in zoos, this is the major issue that prevents them from keeping antivenin on hand and self-treating themselves for a bite. It's not the reaction to the venom, it's reaction to the treatment. LOL
Perhaps, someday, they will develop a synthetic or otherwise more human-friendly antivenin.