You can apply, but are unlikely to be approved.
From the CBP Website:
Q: Should a traveler not approved for travel through ESTA reapply?
A: Unless the circumstances have changed, the traveler will not qualify for an ESTA and will need to apply for a nonimmigrant visa at a U.S. Embassy or Consulate. If you misunderstood the question, or thought something in your background was a reason to be denied and found out later that it was not, we advise you to contact us so we can review your answer. Please go to help.cbp.gov to send an email by clicking on “Ask a Question.” In your email, please explain why you selected "yes" to that question, and ask for clarification on next steps.
So, while technically not for cases like this, you definitely can contact the CBP through their contact form and ask, but you then have to prepare to attach as much proof as you can (you can upload files in the contact form), including official proof of your business, your University degree, your property contract, marriage/birth certificates of any spouse/children you may have, other proof of family and friends...any proof of ties to Argentina strengthening the belief that you will return home.
In addition, attach an explanation letter from your cousin stating why he gave you money, along with documentation proving that it was only for recreational purposes, and that you did not take up employment with a US employer.
It's not very likely it will change anything, but honestly, you have nothing to lose by trying.
Of course, if all else fails, a B-2 visa is the way to go. The good news is they're multiple-entry and valid for 10 years, with the holder usually being granted a 6-month leave on each entry. In addition, if you were refused an entry ban, you can ask to have that ban lifted as part of the visa application.
The bad news is they cost USD 160 and you'll be much more scrutinised, and having been refused entry isn't going to look pretty to the visa officials. If you end up having to pursue this route, bring all forms of documentation I mentioned above, to show them just in case.