Will not nap

My daughter is 6 months old, has one tooth starting to poke through and for the last week she has been extra fussy and not napping/sleeping. We have tried baby oral gel on the tooth/gum and it doesn't seem to help her much. We've gone through every step, is she hungry? No she just ate or it's too early for her to eat, check the diaper & change it, still doesn't help with her fussiness. Maybe she's just going to be a fussy baby, but I feel so helpless listening to her cry so much 😞 Is this normal for a 6 month old sleep pattern to be almost nonexistent? She was up at 4am yesterday, had 1 hour nap 3-4pm went to bed at 8:30 woke up at 12:30 this morning, has been awake since.

Every time we lay her down in her crib, bassinet, or play pen she will fussy so bad, we continue to hold her and she still won't nap.

I don't know what I'm doing wrong as a mom 😞