I'm pretty sure those are non-run-flats. Michelin makes run-flat PSS's, but not in those sizes.
Tires will leak down over time. Mine leak somewhere between a half-PSI and one PSI every two to three weeks. An embedded nail or screw will cause them to leak down faster. Tire pressure goes up or down about one PSI for every ten degrees F.
Get a quality tire gauge. Meiser is the industry standard. They've about $30.
A quality hand pump is less hassle than fighting with extension cords for electric pumps. Topeak makes good pumps under their "Joe Blow" brand. Their mountain bike pump is a high-volume, low-pressure (for a bicycle) pump with a rated pressure of 75 PSI. They're about $70. That's enough to pump up a donut spare on a car.
Let the car cool off overnight. If you have a garage, it helps to open the hood, too. BMWs' engine compartments get so hot and are sealed up so tight that they still heat the front tires after twelve hours. Before sunlight hits the tires and heats some them up, check and adjust the pressures. Adjust both tires on each axle to have exactly the same pressures. Record the data: date, temperature, mileage, and pressures for each tire. Reset the TPMS.
Do the steps above in a week or two, probably after just one week if you suspect something is wrong. If the tire pressures are different on an axle, you probably have at least one embedded nail or screw. Over the decades, I've caught literally dozens of slow leaks caused by punctures this way. I've caught them early enough that I can deal with them in a convenient place and at a convenient time. Attached is a screenshot from my maintenance logbook showing how I caught a puncture early. The right-rear had lost about a fourth-PSI. I looked for, but couldn't find an embedded nail or screw. I assumed I might have mis-measured the pressure by a fourth PSI. The next time, it'd lost about a half-PSI. I removed the wheel to look for a puncture, and... Whomp! There is was!
You're much more likely to get a puncture on the back. A screw or nail laying on its side in the road is not much of a threat. But, the front tire runs over it and causes it to start tumbling down the road. If the back tire then hits it when it's anywhere near upright, you're... well... nailed, or screwed.
The proper way to repair a puncture is to remove the tire and install a "plug-patch system." It's important that the shop has a lever-less tire machine that does not touch (and scratch) the outside of your rims. A tire puncture is repairable if it's not in the outer or inner section of tread.
Think about a spare tire and a jack, since you now know you don't really have run-flats. Bimmerzone.com sells them. Actually, if you take road trips in your car you need a spare even with run-flats.