Under what circumstance can an employee file a hostile work environment complaint?

1) There is no such thing as "hostile" work enviroment. There is behavior that is prohibited, such as harassing or discriminating against an employee on the basis of a protected characteristrics, such as race, religion, sex, age over 40, or disability; however, apart from that, employers and their manager may be nasty, vindictive, rude, etc. Employers do not have to treat employees with courtesy and respect.

2) If you don't have a contract (including a union agreement) or a VERY firm, unambiguous, no caveats (see below) policy statement regarding either discipline or sick days, you can be written up at will by a manager for your use of sick days--as long as its not based on a discriminatory reason (see above). That because without a contract or the equivalent, you are an employee at will, and you may be terminated, suspended, discliplined, etc. at will, for any reason.

3) If you have a collective bargaining agreement, it's terms must be enforced as to both discipline and sick days. However, if those terms are ambiguous, you may need to file a grievance in order to have an adjudication of what exactly they mean--e.g. if you get 10 in November, but can accrue up to 60, how/when do you accrue those? If the CBA is silent on a certain matter, such as disciplinary action for taking more sick days than you've earned, you probably can be discliplined for--contracts, including CBAs, only cover those terms, things, etc. that are within them, and do not necessarily affect matters on which they are silent. You could, if you disagree with the interpretation, again file a grievance.

4) Note that employee handbooks and the like may create contracts between employers and employees but only if they are firm, unambiguous and lack caveats. For example, if a handbook says something like "policies may be changed at will" or "does not create a contract of employment" or anything similar, then they won't have binding effect.