You are acting on behalf of your friend who cannot be here to look at property themselves, correct? You are appointed and asked to do a favor for this person, to be there eyes & ears looking for their next home, of which you agreed. I find it a bit over the top, bordering ridiculous, that you ask for a finder's fee now, unless you already have an agreement. Based on the info you provided & below responses, It does not app[ear that you have a written, formal agreement & it appears as though you can't even get a fee in the state you are in unless you are licensed, so the short answer is no.
You met with the Realtor &" finally found a house". Did you ask to see this particular property or did the Realtor find it based on the criteria of what your friend was looking for? In other words, did you do ALL the research, including pouring through who knows how many listings, set up the appointments to view the homes with the other agents, once a home was found, establish the true market value of the property through active, pending & sold data? Prepare the contract? Set up ALL Inspections? etc, etc, etc.
Who brought up the finder's fee? You? Your friend? If you are doing a "favor" for your friend & there was no talk of money BEFORE they made an offer, then why now? If your friend willing to pay this finder's fee? I don't believe the Realtor should.
You are doing your friend a favor here, don't now muddy the waters on their property purchase for your personal gain. This could get messy.