You did the right thing by filing the UI claim. Wait to see if it is granted or denied. Once the determination is made you will either be granted or denied benefits. Your weekly benefit is determined by your "base period" and will consider your work history in the past 5 quarters so having worked for your most current employer for less than four weeks does not automatically disqualify you from benefits. If your claim is denied, the determination letter will state the reason for denial and you can go from there. It makes no sense to speculate until you have that piece of paper. If you are denied you need to do a cost benefit of fighting it. Typically, if you will get over $1,000 in benefits a month then it is worth hiring an attorney. Often these types of cases are done on a very reasonable flat fee. Hope that helps.
This is not intended to be legal advice and no attorney client relationship exists by virtue of this answer. Your matter may be time sensitive and you may lose your right to purse the matter via the passage of time. It is always advisable to speak with a lawyer and discuss the merits of your claim or defense.
It never hurts to file for unemployment and to consult with an unemployment attorney about the likelihood of collecting it.
The information provided in this answer does not create an attorney-client relationship. If you are interested in his legal services, feel free to call Chris at (303) 409-7635 at his law office in the Denver Tech Center. All initial consultations are free of charge.