I hate splinters!
I have removed tiny splinters simply by soaking my feet in warm soapy water.
I have also heard of these three methods:
1. Ichthammol ointment (also known as black drawing salve)- this is usually found OTC at most pharmacies. You put a little of this ointment on the splinter, place a band-aid on the area and keep it on all day. Hopefully at the end of the day when you take off the band-aid the splinter would have came out by itself.
2. baking soda- what can't baking soda be used for? If you make the baking soda into a paste and place it on the area, it may help your skin push out the splinter on it's own. Your splinter sounds small enough that this could work.
3. duct tape- what can't duct tape be used for? If you know which direction the splinter went in, you can use this method. Stick the duct tape on your toe making sure it is sticking on all areas. Rip off the duct tape quickly in the opposite direction it went in (the same direction you would be pulling it out with tweezers).
I hope that helps!