15 days is extremely young for a puppy to be away from its mother, that said it sounds like you ended up with the puppy from a local shelter, so the mother or a surrogate mother may not be available.
If that is a case I would recommend you go that shelter or a veterinarian to find out the best care regimen for the puppy in terms of diet and socialization. This is going to be a difficult time for both you and the puppy as they will require a lot of extra attention.
Related to your direct question, I doubt that the puppy is trying to suckle from you, and I suspect that it is really seeking warmth and comfort, and is just trying to stay as close to you as possible. Young puppies spend most of their time either in a pile with their litter-mates or right up against their mother, so it is just trying to replicate that with you. In order to keep the puppy comfortable and calm you may want to buy a number of warm and soft plush toys that they can snuggle up with to simulate their typical puppy behavior.
Disclaimer: I am not a vet or an expert on puppy well-being, and you should follow any expert advice you can get on the matter