Hi. Bless him, the world is a really big place, especially when you are so small and have only seen the inside of a house and a garden. Is he used to the lead? ie. did you introduce him to it at home? do you live in an area where there are a lot of cars going up and down the road? if the latter is true try to get him used to the noise of the traffic first, give him a few more weeks to adjust to his new surroundings, 13 weeks is still very young. Can you perhaps take him in the care (if you drive) to the local dog walking park/common etc so that he can see other dogs to take his mind off other things that may be worrying him, he doesn't need too much walking at this age, 5-10 minutes is ample, give plenty of encouragement when walking him, take a favourite toy/tiny bits of food treats (not too much though) to help jolly him along, make sure his collar is on tight enough, you should be able to get 2 fingers under it.
Have lots of fun with your puppy, just go at his pace, if he is not ready to go out for walks along the road don't force the issue, just take him for a few steps, make him sit, make a fuss of him then turn around and go home.
I have just come back with my 4 'horrors',I have been out for an hour it is still only 06.15, can I swap with you??? PLEASE. lol.