I've done too many costumes with fake blood to count by now and I always use my own homemade blood. It really isn't complicated at all to mix up and the results are realistic and beautiful on fabric, although they do make costumes a little bit sticky for a couple of weeks so I would recommend applying it to your costume as far in advance as you can and then keeping the outfit in a garment bag that you don't mind getting a little messy. Since you only want the blood on your shoulder I wouldn't worry at all about the stickiness, though - that's not an area that usually causes too much trouble when it comes to making a mess.
As for the fake blood, here's my tried & true recipe:
Pour about a 1/4 - 2/3 cup white corn syrup into a resealable container. Utilizing about eight to ten drops of red food coloring, stir the color until it's consistent. Add about three drops of green, two drops of blue, and two drops of yellow one at a time and then mix until the color appears to be a dark red/almost brown and looks a deep scarlet when pulled out and dabbed on a paper towel. You may need more or less of each color - play around until you get something that you like. Remember - real blood is a dark red when fresh and a brown when dried. If you want a dried blood look, use more blue and green. If you want something more fresh, use more red and yellow. Once you have a color you like, add a couple of drops of water to liquify the corn syrup and make it a little less sticky when applied.
Here's a couple examples of what this recipe turns out:
// The blood on the left used more blue & green food coloring than yellow and was mixed with a little bit of dirt from the garden & motor oil. I wanted the blood on the right costume to look fresher so it's mostly yellow & green food coloring and is undiluted.
// Another more clear photo of the darker blood
I hope this helps~!