Cessna 150 pilot reported engine roughness during climb while maneuvering away from Class C airspace without radio communication. The engine roughness ended and the pilot continued the flight.

Narrative

I am submitting this report to document two events from the same VFR flight; both of which involved close proximity to Class C airspace and valuable personal learning moments.First event (approximately XA:22):I departed ZZZ westbound and remained just below the Class C shelf (2;100' MSL; using the current altimeter setting provided by the local airport) until clear to the south west (headed towards ZZZ1). Prior to departure; my Stratus ADS-B receiver failed due to a battery issue and would not charge in the airplane. While departing; another aircraft reported being approximately 2 NM northwest of the field. I was flying with a passenger and began to experience slight engine roughness shortly after departure. I chose to fly westbound directly to clear the shelf while climbing to about 1;900-2;000' MSL. I remained approximately 0.5 NM laterally from the Class C boundary until initiating a climb immediately upon exiting the shelf (climb was started approximately 0.5 nm west of the shelf) as depicted on my EFB. Due to cockpit workload (engine concern; other reported traffic; and general task saturation); I did not contact ATC on departure from ZZZ.After reviewing my ForeFlight track log and public ADS-B data; I confirmed that I remained below the shelf until laterally clear before initiating a higher climb. However; I recognize that I could have improved my situational management by contacting ATC immediately after departure using my second radio. In hindsight; this would have provided both assistance and improved situational awareness with the additional aircraft.Second event (approximately XB:31):On the return flight from ZZZ to ZZZ2; I took off towards the northwest from ZZZ and again remained at ~1;900-2;000' MSL to stay beneath the Class C shelf. Having reflected on my experience from the previous takeoff from ZZZ; I decided I would contact Approach without delay during climbout. As I climbed out; starting at approximately 400' AGL (1200MSL) I attempted to contact approach on XXX.XX as published on the sectional; but received no response after several calls even when I was at ~1900 AGL. I then tried XXX.XY (a frequency I had used earlier that day for ZZZ Approach) and was able to eventually establish two way radio communication. However; this did not occur until approximately 10 NM northeast of the ZZZ; near ZZZ3. Upon establishing two way radio communication; I immediately began climbing into the Class C and continued to ZZZ2.During this leg; I was thinking about the engine roughness from earlier in the day and was motivated to fly at a higher; safer cruise altitude; but did not want to climb until I had ATC contact. I'm not sure why XXX.XX was not working; as I was hearing other aircraft and the controllers on this frequency. I had no previous or subsequent issues with the radios. In retrospect I should have exited beneath the class C shelf to the northwest of ZZZ first; and then continued west from ZZZ to ZZZ2. This would have allowed me to climb no matter if I had established two way radio contact with ATC. Upon establishing contact I then would have requested to transition through the class C to ZZZ2.These experiences were strong reminders of the value of early communication with ATC and conservative flying; and I plan to incorporate procedural changes such as queuing up ATC frequencies on my secondary radio during preflight and adjusting my departure planning to prioritize early climbs outside controlled airspace when possible to get myself into a flight profile where I have more time to analyze situations; trouble shoot; and make decisions.In both cases; ADS-B and GPS data confirm I did not enter the Class C airspace without clearance; but the margin was close enough to merit this report. Going forward I will always queue up the ATC frequency in my second radio; and I will always try to climb in a manner that is first clear of aircraft and airspace; and then on course (aviate; navigate; then communicate). Secondly; after some discussions with other pilots; I realized the roughness could've been caused by carb ice; this is now in the front of my mind if I ever experience engine roughness again. Additionally; I will be buying a new Stratus charger.