1. fulfillment ¶
You don't work to achieve a sense of fulfillment; you come to earn money.

There is nothing wrong with this, I just wanted to note that fulfilment with one L ist the British spelling, and fulfillment with two Ls is the American spelling. So, depending on which English you would like to use, decide accordingly.

2. antiquity ¶
Understanding who we truly are is a thousand-year-old question that philosophies began to thinkers have thought about since antiquity.

3. veer ¶
It is not uncommon to see a Justice's (judge in the Supreme Court) veer political leaning veer dramatically during their term.

Or: It is not uncommon to see the political leaning of a Justice veer dramatically during their term.

You try to use the first amendment to defend your client’s discriminativeory behavior.

If you mean: "making or showing an unfair or prejudicial distinction between different categories of people or things, especially on the grounds of race, age, or sex", the word that is usually used is discriminatory.

5. nuisance ¶
Holding a drink in my hands is a nuisance during shopping.

There's nothing technically wrong with saying "holding a drink in my hands", but you probably would only be holding it with one hand.