- The air passages in your throat and lungs swell shut so severely that you cannot physically force air in and out. Within a matter of minutes, you will loose the ability to breathe. Period.
- At the same time, your blood vessels are rapidly dilating, causing a dangerous drop in blood pressure. This is why its commonly called anaphylactic shock, because your blood pressure has dropped to the point that the blood cannot adequately perfuse vital organs, namely your brain and your heart.
So between the fact that you can't get oxygen into your lungs, and the fact that your blood can't deliver oxygen to your brain, and the fact that you feel like shit, and know very well that you're in the middle of a life-threatening emergency... you don't really have the capability to perform tasks requiring concentration and fine motor skills, such as would be required to manually draw up a precise dose of medication into a syringe and inject it into yourself.
An EpiPen or similar device is "necessary" because it is an incredibly simple mechanical device that you can operate even while in extremis. You pop a cap off both ends, and push it against your butt check. Its something that anyone, even children, can be trained to do, and to practice (obviously with a dummy device with no needle or medication). And practice until using it practically becomes a reflex, and not something that requires concentration to perform. Its easy enough to do that, even when overcome with anxiety and decrease oxygenation, people can usually manage to work an EpiPen.
I suspect you probably haven't actually experienced anaphylaxis, if people had time to talk to you and for you to convince them that everything was fine. Anaphylaxis requires rapid administration of epinephrine. So you may have had an allergic reaction, maybe even a bad one, but unless you actually experienced the sensation of being unable to force air in and out of your lungs, even when trying with all your might, you haven't truly experienced anaphylaxis. I'd also take issue with your assumption that administering an EpiPen is a "high risk emergency procedure." I suppose there is some risk of local infection, but I'm not aware of any documented cases of infection, at least anything requiring treatment, as a result of an EpiPen. (There are other risks associated with Epi administration, but infection is effectively not one of them.)
So some sort of autoinjector device, be it an EpiPen or a similar competitor, is effectively required to be able to safely manage anaphylaxis.