Fair Use
Generally speaking Fair Use allows you to use an image because the public has a right to know and/or to speak out to power. For example, you can often (but not always) in a news publication, publish someone else's photo of a disaster or a photo of a politician in a funny hat (like wearing a lampshade, in a bar without pants.) Interestingly, the rules on whose material you can publish - other than your own - are different depending on whether or not the image is published on the Internet, in a newspaper or on a t-shirt. It's likely that you have less right to fair use of an image on a T-shirt than on a Website because a million people probably have more right to know something than you have a right to collect $5.
Also, you can - sometimes - publish or sell a photo of an individual as long as it is clear that the individual isn't endorsing anything for you. For example, paparazzi sell photos of celebrities to publications all the time. If you use that photo, that someone sold to a publication, and it's not considered to be in a fair use situation, you will likely be in a world of hurt. Prepare to lawyer up.
Also, photographs that are of a certain age may (or may not) be in the public domain. Some images that are in the public domain, are for sale.
Finally, you may have all the right in the world to publish a photo, but someone who has an interest in that photo may try to shut you down. You may or may not want to fight. For example, I printed and put up for sale, an image of an exotic car on a public e-commerce site. I took the photo of the vehicle myself, on a public street. It happened at an event (on the public street) and there was even a sign that said photography was permitted. An agent of the exotic car manufacturer complained to the e-commerce site and I had to remove the photo - or faced the possibility of having my other photos being removed. So I removed the photo.
So, are you allowed to print anything or nothing? Sometimes.
What do we do? Well, we certainly can't afford to consult an attorney every time we print an image. (Certainly, we buy images, but the rights on those are spelled out. Mostly.) But in our (and therefore your) business, we believe it's important to read as much as we can regarding the law, then make our decision on whether on not to use an image.
Is my reply helpful? Thus far, probably not. Except there is one other thing that we have started to do recently. Google has a really good image search. So, before we use an image that we think might cause a problem we usually do a Google image search. For example, you could upload a photo of a design on a T-shirt. You would be amazed to find how many so-called "Orphan works" have "parents!"