If I shared my prescribed medication with a co-worker who was subscribed the same medication and does because she forgot hers and was in terrible pain, is this grounds for termination?

Yes, it is grounds for termination. First, to be perfectly clear: unless you have an employment contract limiting the reasons why you could be terminated (and this was not one of those reasons), you were an employee at will and could be terminated at any time, for any reason whatsoever--that is, your employer could just decide to terminate you at any time.
Moreover, what you did was very dangerous: you are not a doctor and should not be giving someone medication--especially pain medication--even if you believe it was the same medication. The other employee would have had a very bad reaction; could have overdosed; could have had judgment impaired and hurt herself or someone else at work; etc. And if this was a controlled narcotic, then you also violated the drug laws: no non-doctor may dispense narcotic medication. What you did exposed your company to risks or problems, such as potentially dealing with an overdosed employee or one with a bad reaction or behavioral issues at work, and also could possibly have brought about drug charges (if it was a narcotic) against an employee, which would have at least disrupted work; you had no right to do this to your company and showed poor judgment, and your company would be justified in terminating you. 
Your co-worker should have gone to an Emergency Room or immedi-center or to her doctor to get a new prescription or refill; getting prescription medication from you was not approrpriate, especially at work.

Yes, no matter how well intentioned (although ill advised) your action was, you can be fired for this. In fact in an at will employment relationship an employor can fire a worker for this reason, any reason or no reason at all, with or without notice. The fact is that employers can set the terms and conditions of employment much as they see fit; this inlcudes who to fire and when. Accordingly, unless you are afforded protection under an employment contract, union agreement or even company policy, you may be terminated.