Poor baby...sounds like my oldest son. I have let him stay home on days when his eyes were swollen and he looked and felt like hell. He's older now (14) so more often than not I tell him to suck it up and get to school, but I do let him come home if things are really bad.
He was on Claritin starting at age 3 and that stopped working well a few years ago. Now he takes Zyrtec and eye drops (Opcon-A or Naphcon-A or something like that) and then on his peak days when that doesn't work, also I throw everything else at him - chlor-trimetron, benadryl, other non-drowsies like Claritin or Allegra, etc. This is all with his doctor's blessing, of course.
I think the idea below about washing her hair and having a fresh pillow case at night is a good idea, and would make sure that her windows are closed in her room. It might be a good idea to get a small air purifier for her room as well - it seems a little unusual that she would wake up with the swelling vs. having it occur during the day. My son usually starts off the day functional and then by late morning is a total mess. It might also help to give her Benadryl before bed - it will give her system time to calm down overnight while she's sleeping anyway and may reduce the swelling that she gets early in the morning.
ETA: someone recently shared a tip with me about using a nasal spray for him as well - the idea is that you can coat the inside of the nasal passages with stuff that will collect some of the pollen and prevent it from getting into your child's system and triggering the immune response.