You can certainly ask them to pay your medical bills. If they do, you'll save the expense and hassle of using an attorney. However, they (or more likely, their insurance) may be reluctant to pay, because there are a couple of things going against you: first, you're out of town, so it'll probably be more difficult for you to deal with the store. Second, you weren't injured badly enough to require immediate care (you went home somehow, and to the ER later).
If you didn't get a copy of the accident form, you should try to get one as soon as possible. Keep copies of all paperwork related to this (E.R. bills, etc.) And don't just call the store -- write them a letter asking them to pay your medical bill.
If you don't get anywhere in a week or two, you'll probably have to hire a lawyer.
Yes. You should ask them to pay.
Most retail establishments have "med pay" insurance. That insurance is a no-fault insurance that covers medical bills only. It would not cover any other losses you might have had. It sounds like you have a relatively minor injury, and that might be good enough for you.
If, on the other hand, you lost time from work or had other losses, then maybe you will need to go beyond med pay coverage and assert a claim. Keep in mind the statute of limitations, which in Oregon, is two years for injury claims against non-governmental defendants.
Jeff Merrick
http://www.jeffmerrick.com
The above is not legal advice. I cannot give you reliable advice without knowing more information. It is intended to raise some issues for you to discuss with your own lawyer.