The bright line standard for trademark lawsuits is essentially "would a reasonable person mistake your brand for your competitors?". In this case, based on what you have said here, you have taken your competitors name, and added "my" in front of it. So most reasonable people would conclude that it is highly likely someone will mistake your competitors brand for yours.
If you were in a completely different industry than the similarly named company, then there would be some wiggle room, because you could argue that even if someone was initially confused about the two companies, there is no possibility for them to buy your product thinking it was the competitors. However, you are in the exact same industry, so the likely conclusion is that the customer will be confused and likely to buy your product thinking its your competitors.
Unfortunately, the domain name issue is irrelevant in the face of trademark law. In fact, as has happened with many other infringement suits, it is likely that if you lost the lawsuit, you would be forced to transfer the domain to your competitor.
