can’t leave the house or even go upstairs

I have a 3 month old puppy which has been with me for one and a half months. Everytime I try to leave the house he cries and yells and barks. He follows me everywhere in the house and repeats the same patterns with my sister, for example if she leaves the house he goes to the door and cries and cries until I pick him up. He doesn’t even nap if it isn’t next to me. I’ve tried ignoring him but he whines for more than 15 minutes and I just give up. Please help me what am I doing wrong?? Is this normal for his age does it get better? How can I help him be more independent? I’m out of work right now and am able to spend almost the whole day with him and just leave when my sister comes home but when I’m back to work he will be alone (not completely cause I have two cats) and I’m worried he won’t be able to handle it. I feel like the worst dog mom ever like I’m doing everything wrong…