OP,
I'm going to weigh in my .02. Firstly, I don't know what state you are located in, so it's hard to give accurate advice...so where are you? I'm going to give you some advice from my state, California and from the standpoint of a non UPSer (so no one kill me please). Here, no matter what your injury is, you MUST claim all injuries immediately to human resources or you could lose your job. This is to protect both employer and employee and to get the employee evaluated A.S.A.P. As this is the standard, it rarely happens because most people need the money. Workers comp will pay for all medical visits, prescriptions and 66.6% of your paycheck, tax free and keep your medical insurance going. I know you guys have contracts and unions, so it could be different. Also, your sup coerced you into signing a paper, and I'm very sure that is illegal in all states. You should have had some time to read, think, reread and maybe have a rep with you for back up.
BUT... this is where the law comes in. If you wait for "peak" season to make more money and then back date your claim, when it goes to court, it's going to look fraudulent and you will be raked over the coals by attorneys as to why you didn't file right away and end up with nothing. Workers comp attorneys are very different than your average family law, or any other attorney, they are governed differently by the court system and go to extra effort to find discrepancies.
Are you a part time doctor? (sorry for the sarcasm) If not, please let a licensed M.D. evaluate you and make the determination of your injuries. I say this with such vim and vigor because of my own injury. I used to work a 75 hour week making the almighty dollar and I got hurt. I loved my company and I only asked them to pay my ER visit. I thought I was healed, but a year or so later I needed surgery and I never was the same. So thousands of pain pills later, doctor visits, etc., I'm wondering "what the hell"?
So maybe for your own good, take care of you first?