Is there any natural way to see if I am anemic without a blood draw?

No. Anemia is a condition when your hemoglobin is less than a normal range. Blood draw to check your hemoglobin level needs to be done to check for the level accurately. Some clinical sign and symptom for instance- pale, feeling weak, fatigue, dizziness may give you hints or consideration that you may be anemic but they wont tell you for sure. See your md and have yourself checked.
Exam. Looking at the conjunctiva and if they look pale probably anemic. If severe and long standing, one can have "spoon nails." the finger nails look like spoons. Lines on the hands are usually red or pink but if anemic, they are not. However, you can't tell the level so a blood draw would still be needed. Hope this helps.