You're not screwed. Just unbolt the cover scrape off all that red stuff with a razor blade, get some black rtv and seal it back up! It's a pretty easy job, maybe look for a step by step on YouTube if you're not familiar. I just did this on my jeep, took about a half hour.
Here is a video I found on YouTube, it's for a pinion replacement but he also re-seals the differential cover too. The video is a front differential, but the process is the same. Good luck!