Inner tubes burst for more reasons than just punctures. The tire might in fact be in perfect condition with no puncture.
You need to pull one side of the tire off the rim. Mark the valve stem position on the tire first. Then remove the tube. Mark it or remember how it is oriented. Lay in on top of your tire, then try to put some air in and see where it might be leaking.
Once you find that location, then is it on the tread side? The side wall or the spoke channel side? Once you know that you can start pondering why it flatted.
Any chance it's been several weeks since you had the tire replaced and maybe it was at too low a pressure for riding and you cut the tube with the rim while rolling on it?
Any how... I've probably had more flats in the last 15 or so years that were my installation errors than I've had flats from punctures.
If you aren't the DIY type, then you need to go back to the shop. No embarrassment for that if that's you. Some people don't need to do their own DIY. It's not as simple as those that have lifelong skill doing it make it out to be.