So I was at the Fort when I told her to go see the Dr.
It's now two real-life days later, and I'm pretty sure she's never getting there.

However, this also means I can't finish Rex's quest. :\

Any idea how to find her or fix this? It's the second huge glitch I've encountered - the first one forced me to remake my character, and this new one is screwing up my two favorite companion's quests. I'm pretty disappointed. :[

Don't know, but I did lose Rex for awhile. I found him at the School of Impersonation. Try walking the route between using the perk from ED-D, see if Lily (as a friendly marker) pops up on your radar. Time consuming yes. but what can you do.