She could get a tooth before 6 mo, it's not unusual!
Sounds like her teeth are moving under the gums which does cause a lot of discomfort and can contribute to night wakings
At 4.5 mo there are loads of developmental things going on too, so that will unsettle some LOs and cause night wakings and/or short naps.
If there are any other signs such as patches of eczema or tummy trouble then it could be diet related (yours if she's EBF).
DS had plenty of 'teething' episodes well before anything appeared as his teeth moved below the gums, but they didn't last more than 2 or 3 days then he was back to normal
Hopefully she'll be ok again in a day or so