First, learn to change your own tubes. It's not hard, and you really should be able to do it. Because, frankly, if you're taking this same bicycle to the same shop every few weeks for them to change a tube, and they're not taking the time to really solve the problem, they're ripping you off.
Because it seems like they're not even trying to find the cause. They should remember you bringing the same bike in every few weeks. That's especially true if this is the same shop that replaced your rear wheel/rim.
Also, you need to be able to take a tire off to really solve problems like this yourself - in less time and for less money than it takes to haul your bike to the bike shop, and then go back and get it days later.
Now, for why you keep getting flats after a few weeks - something is slowly working its way through your inner tube. It could be in the tire; it could be somewhere on the rim.
First, are you inflating your tubes to a high enough pressure that they don't get pulled around the rim? If your valve stem keeps going cockeyed and gets slanted instead of staying upright where it pokes out of the rim, you're running your tubes at waaay too low of a pressure, and the tire and tube are slipping around the rim. But the valve can't move, so the tube pulls at it and is quite likely to tear and fail.
Another possible cause of flats related to using too low of a pressure is something called a "pinch flat". A "pinch flat" happens when you hit something and, because the pressure is low enough, the tire gets compressed to the point that it gets pushed hard into the rim. The tube gets flattened and pinched between the tire and the rim, literally cutting holes in the tube. The holes are usually paired because the tube when the tube gets flattened, both layers are caught between the tire and rim and two small holes get sliced into the tube. Pinch flats are often called "snake bite" flats because of the paired holes.
Pinch flats are more likely when tire pressure is too low - it's easier to compress the tire enough to pinch the tube.
IMO, you're not likely getting pinch flats - those are usually pretty clearly related to hitting something hard enough that you notice it, and then your tire(s) are immediately flat. I suspect if that were the case, it would have been noted in the question.
If you're not underinflating your tires, get the failed tube off, and find the hole. You now know just about where in the tire or rim the problem is likely to be. (This is one reason why experienced cyclists and bicycle mechanics always mount a tire with the label at the valve hole - when you get a flat, it's possible to determine where the cause is...) The hole may not be exactly where the cause is - the tube can be stretched and twisted some inside the tire, but it should be in the same general area.
Check the rim - it's easier and faster to check the rim thoroughly, and given your flats likely started after a wheel change, IMO the most likely culprit. Start in the general area where the hole is.
Look at the rim tape - the strip that covers the spoke holes in the rim. Is it evenly applied? Does it cover all the spoke holes properly? Is it bulging badly into the spoke holes? Is the rim tape torn or cracked anywhere?
That's the most likely cause, IMO. If a spoke hole isn't fully covered, the tube will bulge into that hole and the slight flexing the tube undergoes when you ride will slowly cause a hole to form.
Are there any too-long spokes protruding through the rim tape? That's also a likely cause for your symptoms, and also could be from a new wheel that wasn't properly built.
Check the valve hole - look for sharp edges. Another thing that can come with a new wheel.
If all that looks good, look over the entire rim, searching for something wrong. Are there any cracks? Anything protruding from the inside of the rim that could wear a hole in a tube in a few weeks?
If it's not the rim, something could be embedded in the tire - to find it, remove the tire, then take a cotton ball and, without pushing it hard against the tire body and being sure to always leave a little space between your finger tips and the tire body, rub the cotton ball all over the inside of the tire, in both directions at least.
Things stuck in a tire can be sharp. If you use your finger to look for anything penetrating the tire, you're likely to find it by noting the bloody thing that tore a hole in your fingertip. It's better to find such things by having them catch a few threads from a cotton ball.
Now, that may not find it - something could be embedded into the tire in a way that it only pokes out when the tire is flexed, like when it rolls over the ground. Turn that tire inside out and flex it, and recheck the entire inner surface of the tire looking for cracks or things that poke out or that grab a few threads from your cotton ball.
If all of that doesn't find the problem, get a new tire. In my experience, older tires can lead to frequent flats. You may also simply need more puncture-resistant tires because of how and/or where you ride.
