You may have varicoceles, which are dilated veins around your testicles, often described as a "bag of worms." These typically increase with standing and decrease when you lie on your back. These are more commonly seen on the left side, which matches your clinical history. To rule out varicoceles or other pathology, consider scrotal ultrasound.
My theory is that when you wonder about something especially regarding your crown jewels/testicles, that it is good to see a doctor and get examined. You probably have retractile testicles. This is when the testicle moves back and forth between the scrotum and the groin. However, what is throwing me off is that it just started with you and you aren't a baby. It's usually a young person problem that goes away. What causes it then is an overactive muscle. Here's information about it. https://www.mayoclinic.org/diseases-conditions/retractile-testicle/symptoms-causes/syc-20377197 But again, that's usually little ones and you are an adult and this just started. I mean, there is the whole cold temperature thing which is well known for causing the testicles to get tight. Some guys get this during sex too. And maybe you do as well during your bm. Issues with the cremaster muscle? This is the muscle that reacts to temp changes. If this is a new thing that is happening, your best bet is to see your doctor for a quick exam. Let us know what you think and they say.