I bumped into a display shelf in an Ohio retail store that caused my shin to bleed profusely. Store employees helped bandage my leg but the bleeding continued, off and on for several days.
The leg became infected and swollen causing severe pain. I made multiple trips to the doctor for treatment. Most of the expenses (approx $3500) were covered by insurance.
Do I have a cause for action to recover co-pays and pain and suffering? The store is ignoring my complaints to them.

Yes you have a cause of action. Call an attorney. Find one in the yellow pages.

Do I have a cause for action to recover co-pays and pain and suffering?
It has been my experience that just about anyone can file a petition citing that they have a valid cause of action against a defendant.

I believe that what you are looking for is will you be able to successfully recover damages through taking legal action.

The simple fact that you injured yourself on someone's property in and of itself does not obligate the property owner to pay damages for the injury. You would have to be able to establish what standard of care the store owner owes to you, an invitee into his store, and that the standard was breached. In other words, your challenge is to prove that the store was negligent in some way and that store's negligence was the cause of the injury.

I am curious to know what kind of display shelf we are talking about. (Is the actual structure of the shelf a foreseeable hazard? Was it positioned in a manner that would be a foreseeable danger? Was it some sort of protruding shelf that was not in plain view, etc..)

The advantage that you have is that a business such as a supermarket has a very high standard of care to it's patrons or invitee's. You are an invited guest in the establishment for the purposes of the owner's economic benefit.

I couldn't give you a definitive opinion on your chances of recovery without having an answer to the above questions. What did the store owner do wrong to cause the injury?

Hard to say because you bumped into the display meaning that likely more than 50% of the fault would be yours, so probably no recovery for you. However, consult an injury attorney to discuss your situation.