There's a fundamental problem with your code. Try this test were we compare my solution with yours (choosing all numbers from a space of 100 available choices.
import random
SPACE=100
print("First test")
total_choices=list(range(SPACE))
random_list=[]
for counter in range(SPACE):
index=random.randint(0,len(total_choices)-1)
random_list.append(total_choices.pop(index))
assert len(random_list)==len(set(random_list))==SPACE
print("End of first test")
print("Second test")
randomList = []
for counter in range(SPACE):
randomInteger = random.randint(1,SPACE)
while(randomList.count(randomInteger) > 0):
randomInteger = random.randint(1, 10)
randomList.append(randomInteger)
assert len(random_list)==len(set(random_list))==SPACE
print("End of test")
My code completes the task while your code hangs. If you use that code at production then it can create a serious problem like hanging the entire application.
The important question is: Do you understand why your code hangs with that simple task?