With any long term injury, See a professional first. Be it a GP, physiotherapist or something else.
Now for the chatty part.
Where exactly does it hurt? At the back of the heel? Somewhere up the back of your leg leading up to your knee?
If it happened to me, I would examine what I was doing leading up to the injury (find the cause) and figure out if I did movements incorrectly (or in a way to cause the injury).
It could be something like too much jumping, landing in the wrong order or maybe lunging with poor form “going over your knee”.
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You’ve already identified that you didn’t do much of a warm up. In future make sure to warm up either before you get to the courts or before you play.
A small jog, a jog with “high knees”, a jog where you kick your bum is usually enough for junior players to warm up. You could do running, moving around court(s) along the lines with sidesteps / lunging and specifically for Achilles you could stand on a wooden bench and slowly lower your body off of it (toes still on the bench).
And make sure you have appropriate footwear. There is a lot of dynamic and fast movement and changing direction in badminton. Protect yourself 