I too have checked & have been told it's ok to use both panadol & nurofen together as mentioned. However I only do this in extreme cases.
Can you see any lumps or white lines, is bubs drooling heaps, tugging on ear, have a temp, fussy eating. Usually teething has these types of signs or other symptoms than just not sleeping.
ATM we think Charlie is teething, though isn't completely off his food, so just using bonjela & working fine for sleeps. And for the record Charlie hates it & it's a pain to get him to take any teething gel so we use an applicator.