I got the injector from Sir Hammerlock, injected the pod and this huge green badass thing popped out and killed me in the face. Now I can't find it nor can I inject another pod to achieve the same effect. The quest is still active asking me to kill the mutated varkid but it is no where to be found. What am I to do?
You can make more Mutated Badass Varkids; just inject another pod by using the Action key (E on PC). It does not show an action prompt for this, but you can still do it. You won't know if it worked until the pod hatches, just get as close as possible and press E/pick up a couple of times and wait for the pod to hatch. Since there's no visual indication, get ready to fight a Mutated Badass Varkid immediately after trying to "inject" a pod in case it worked. They deal Corrosive damage, resist corrosive (IIRC) and are weak to Fire.
You can also spawn multiple mutant badass varkids at once if you want to speed up the process. I strongly advise against doing that unless you're significantly overleveled for the quest (I take it you aren't).
You'll have to do it several times to make more mutants and kill them. It's awkward, but unless you've caught a glitch, it's still possible to hatch multiple mutant varkids. You don't need to find the one you made before (he's despawned by now and that's okay).
I had the same issue but after leaving the area for about 10-15 minutes and going back I finally got the prompts back.
Keep in mind you have to let the larvae go into the pods and then the command prompt comes up. If you mess up an adult comes up and if you wait even longer the adult eventually turns into a different (non-mutated) badass form.