Do you need a logo made or wanting someone to increase the resolution for you? If you're look for the latter of the two, you can't really "add" pixels to an image to make it a higher DPI. You can only do that if you shrink the image to where to pixels that are there, aren't stretched so much.
Well, you can't really do that simply because you can't add to something that wasn't there in the first place; that's kinda of like asking how to convert a 100 page book into a 150 page book. What your best bet would be is to get a higher resolution picture of your logo and then enlarge it, that way, the pixels are there to fill in the spot.
While it wont be perfect, you can resize your current logo, within a equal ratio, and then use a sharpen tool to make the picture less blurry. It won't look too good though, especially on a shirt.
Making a logo is not a big deal, but the big thing is to make it in a proper way and make it in a high resolution that’s where most of the folks fails to do so. There are plenty of logo creation site available which makes easy to build your business logo. If your logo looks blurry or it is not up to the mark as you would like to be, you are probably designing the logo in too small of a canvas size. When you start off designing your logo, be sure to choose the right canvas size and then start getting creative with your design.
It's not a perfect solution but if you convert the bitmap image (original logo) into vector art, you can size it up/down as much as you want with no loss.
This is the reason so many logos are made in Adobe Illustrator vs Photoshop.