I track my heartbeat during each training session for atleast a year now. I only get out of breath, when I approach my max heartbeat and my heart is obviously not able to keep up with the oxygen demand.
An other observation is, that double/single and the pace of the match have a major impact on my heartbeat. Doubles is almost always in the range of 70-90% of my max heartbeat, standard single is almost always above 90%. 90% matches will exhaust me quite quickly after 30-40mins, whereas 80-90% matches can go on for hours.
So I guess, that your fitness is not yet able to keep up with the pace of these matches/training sessions.
I would recommend two things, first off visit a doc and lets check your health condition, you just don’t want to risk any health issues with your heart considering that you are already not that young any longer and that badminton is a very demanding sport. And check out the Polar OH1, a very precise pusle sensor (almost as precise as a belt, just forget about any pulse sensor clocks) which is really easy to handle (just wrap it around arm) and do not need a connection to your smart phone during activity.