How do I tell if the pain coming from my butt is sciatica or an internal thrombosed (blood clot) hemorrhoid?

If Rectal pain. then hemorrhoids likely. If in buttock area then likely spine related, only way to know about spine issues is get lumbar spine MRI.
Location. Hemmoroid pain will stay rectal. Sciatica pain generally starts in the back and then travels down the buttock to the toes, someimes associated with leg numbness and weakness.
Easy. Hemorrhoidal pain is local at your anus usually, sciatica usually radiates down your thigh to your calf/shin. Also thrombosed internal hemorrhoids are very unusual and otherwise internal hemorrhoids rarely cause pain. External thrombose often and do cause pain. You should be able to tell the difference.