"We all feel a bit tired."
Thank you, ted202303 And the "overstuffed" Chinese solution still stands as "confusingly overstuffed" ......... Here, at https://resources.allsetlearning.com/chinese/grammar/Comparing_%22youdian%22_and_%22yidian%22
clearly, there is no need for 觉得 ， They give this example: Wǒ jīntiān yǒudiǎn bù shūfu. Today I don't feel very good.
So, for us here, the right answer is: 我们都有一点儿累
觉得 is used in other contexts, for giving an opinion, not a tentatively diminishing qualifier on one's health/state of mind.
Takers, anyone? What do you think? Remember, Chinese IS NOT LIKE FRENCH! (I am French) The French love to complicate sentences with lots of "add-ons". The Chinese, on another hand, clip the language to its bare-bone necessity, removing unnecessary words whenever possible. This is why Chinese poetry is such a difficult art . . . . . and so sublimely beautiful when it succeeds . . . and so, so difficult to translate, for the same exact reasons . . .
Its a grammar structure.
Have a look at this site for a better understanding of why 有 needs to be there