He has no real competition so I feel like he is just trying to scare me away so he has all of the market to himself.
It is possible, certainly, that the owner of Pawz, if this is the "Natural Pawz" company you are speaking of, is trying to scare away competition by sending out cease and desist notices with nothing to back them up legally. It is also possible that the personal contact with you was the first step before a cease and desist or a lawsuit.
But here it really matters who exactly contacted you - a company with a federally registered trademark or a small-time artist selling a similarly-designed tee-shirt online.
Trademark holders must be vigilant when it comes to policing the marketplace for possible infringers or they can lose all rights in their marks, and sometimes they may see infringement where none exists. Copyright holders will not lose their
rights to infringers but they can lose revenue, so they likewise can be vigilant.
Without seeing the tee-shirts in question, it seems
possible (if not entirely probable) that consumers could be confused as to the origin of your goods and believe your "Love Your Paws" is connected with the federally registered company. This could make any warning or cease and desist notice from Natural Pawz a legitimate warning of infringement. Your paws with heart image might be substantially similar to one marketed by Natural Pawz.
With both generic word trademarks and images like hearts and paw prints, it will be the substantial similarity between what is created and used (similarity in the names, slogans, designs), and consumer confusion that is generated as a result, that can create a problem. Otherwise, anyone can use the word "paws" and anyone can draw hearts and paws. Without a personal review of the tee-shirts being marketed and research into Pawz and its products (or into whoever sent you the notice), it is impossible to say if you would be well-advised to cease and desist as demanded or if you can go ahead with your tee-shirt sales without fear of losing an infringement action.
As a note, I haven't done any research into the Pawz company or its products, or researched any tee-shirts being marketed using hearts and paws images.