Hello, and welcome. I am a licensed attorney and happy to assist.
I'm sorry to hear you were injured, but happy to say that you may have recourse. If you fell inside your apartment, because of a defect of which the manager aware that was not timely repaired, the management/owner of the building is responsible for your damages. If you fell outside the apartment on a dangerous condition of the property which was either previously reported or of which management should have been aware, they are still responsible for your injuries. It doesn't matter whether or not the manager believes you fell. The fact is that you did. The manager is looking out for his or her own best interest by failing to recognize what happened and, in that manner, is trying to intimidate you from not seeking assistance.
Under the circumstances, it would be prudent to consult a local personal injury attorney, who will provide you with a free consultation and review all of the information you provide, as well as photographs of the condition that caused you to fall (that's important, if possible). Do not be dissuaded by management - a direct attorney is vitally important to ensure your injuries are properly treated and you are compensated for the harm they have caused. You have significant legal rights here. A good referral source will be your County Bar Association. There will be no charge for that referral, and no charge for the initial consultation with the attorney to whom you are referred. If the attorney takes your case, there will be no out-of-pocket fees and expenses to pay, either. It's a win-win situation. You can either call directory assistance for the Bar Association referral contact info, or let me know your city and state and I'll be happy to provide it for you.
I hope this helps. If you need additional information or clarification, please let me know and I will continue providing assistance. If I have addressed your concerns or pointed you in a positive direction, please remember to leave a positive rating when prompted, as that is how attorneys on this site are credited for the help we provide.