1. Wages are a small portion of the total cost of everything. For example, for a place like Walmart, the bulk of their costs is the products themselves (a lot of which are not even manufactured in the US, and thus not affected by minimum wage changes). The costs of running the stores can't be all that low, either. Increasing wages to $15 wouldn't make a huge difference to prices. They might go up a slight bit, but... it's simply not going to be that much.
2. Only 2.3% of hourly workers are paid the minimum wage. [0] (Although obviously, if increased to $15, then everyone below $15 becomes a "minimum wage" worker, meaning the percentage will be a bit higher) When you talk about increasing the minimum wage, you have to realise you're not actually increasing wages for everyone, only a small portion of people. Increasing them will not increase prices all that much, since it doesn't affect that many people to begin with.
Some prices would go up a bit, yes. But a lot of companies wouldn't be affected in the slightest, and so their prices wouldn't change, meaning the overall effect wouldn't be all that pronounced.
[0]: https://www.bls.gov/opub/reports/minimum-wage/2017/home.htm