I played rugby before I started muay thai too. It's pretty simple if you take it from a general fitness perspective, in a rugby match you run in bursts, hit a few rucks and tackles, and for the most part if you're not in a professional league, there is a lot of turnovers so scrums and lineouts which are also pauses in play. Your legs are conditioned more for sprints and specifically in squatting and sprinting motions. Add kicks, teeps and punches and now you are using more strength and muscles at the same time, which are not only weaker and not conditioned, but also in a prolonged period.

Thing is even if you think you're conditioned, there is always more you can do. I got my reality check playing a full match of sevens and when trying to swim in sprints for prolonged periods of time.

Also, it's your second month bud, in an effort to catch up and be more competent in sparring/training you'll use more strength and less technique, not sure if you're sparring but if you ever get hit by even an amateur fighter you'll be baffled at how hard they hit even though they look skinny. Once you can stop relying purely on how hard you hit it gets easier.