Actually your flow is fine, it's just that your tampon is sitting on the same side in the vagina and so blood trickles onto only one part. Here's how it works: At the top of your vagina is your cervix which is the opening to uterus and where your period blood flows out from the uterus into the vagina. At the top of the vagina near the cervix there is a bit more room than down lower to accommodate the head of his penis when you have sex. When you put the tampon in, it may not sit exactly underneath the small hole in the cervix but rather off just a bit to one side or the other. When your period flows out of the little hole in the cervix, it tracks along the side of the tampon rather than the central top area so the blood only appears on one side of the tampon. No worries!
This has happened to me before, but I attributed it to just a lighter flow. You did not mention that you were in pain so I would not worry especially; just check out health expert Dr. Molly’s answer.
Rest assured, you’re not bleeding from one side! The reason why half of your tampon is soiled may be due to sheer coincidence, or it may be due to changing your tampon too often. Sometimes changing your tampon too often can lead to some illusions such as one side of your tampon being white or even all of it being white (leading you to think that your period is over when it’s not). It doesn’t mean that that side of you is bleeding; rather, it means that you left the tampon in there long enough to catch only that amount of blood which happened to fall on that side. It’s recommended to change your tampon every four to eight hours – more frequently if it’s a heavy flow. But because there’s some white on your tampon, it seems that your flow isn’t too heavy, so let your tampon sit up there long enough to soil that other side of it (or switch to a lower absorbency).