Student pilot flying a C-150 aircraft reported alternator malfunction in flight.

Narrative

Solo cross country flight (short)Upon take off from ZZZ the radio lights began to flicker. I turned them off and checked the masters and fuses and found no problem. Turned the radio back on and it was still blinking. I ran my checklist at this time. I was on the crosswind section of the pattern and decided to stay in the pattern with minimal power and land as soon as safely possible to investigate the issue. After landing I turned the engine off. It would not start. I called my CFI and told him that I was broken down in ZZZ. I then called the flight club and told them that I was also broke down in ZZZ. Upon preflight inspection I could not feel the alternator belt and reported this to the safety officer at the club. They messaged that they were sending someone to get me. An hour passed and then they said they were sending a plane with recovery pilot to me. Finally after 3 hours they said that they (Safety; Chief Pilot instructor; my CFI and Maintenance) had discussed it and it was fine for me to fly the plane back under VFR rules. The planes battery was charged. I started the plane and sent a message that I was leaving ZZZ and for someone to please watch FlightAware and text me if there was an issue.My CFI instructed me in challenges of no flaps landings; how to avoid getting lost and what to do if that happens; we discussed flight altitudes and best ways to spot potential places to set the plane down if an emergency did arise. I was instructed to reserve battery power for emergency radio communications and squawks. I have flown Aircraft X for appr. 70 hours and I was confident in her ability to make the trip. I have flown the same trip with instructors 4 separate times and I'm familiar with the terrain. I departed ZZZ at XA00 and landed safely in ZZZ1 at XB35 (appr). Name from flying club was waiting on me and making radio calls while I was entering the pattern and landing. The flight was made without any other events or incidents. I felt safe in making the flight and confident that I followed all safety rules applicable.