If I got hurt at work, can I sue for negligence?

The "good" thing about personal injury actions are that consultations with an attorney are free.  You should indeed set up a consultation with an attorney as soon as you can.  Slip and fall cases - like most personal injury cases - depend on the facts and circumstances surrounding the accident.  Notice, for example, of a condition - unless you create the condition - is one of the issues that needs to be determined.  Damages - which you appear to have - is also an issue.  Seek consultation also because you may be limited to workers compensation if it happened at work.  That is the general rule with work related injuries.  Good luck to you.