My dog used to have more issues. I find that pumpkin really does the trick whether he is constipated or has the runs.
To solve the actual problem though will take some detective work. I have found that when he had any fleas he would have stomach issues. I am not sure if it was from ingesting fleas or a contact allergy. Also, certain grasses can bother him and make him chew his skin to bleeding, and this tends to come with the runs as well. Finally, for him, I found that I need to minimize grain. I do give him grain-free food, but he still gets grainy treats. I find that completely grain-free is not good for his stomach, but reducing it to just treat time made all the difference in the world for him.
Of course, that is what works with MY dog, and your dog will of course have different triggers. It may be something else as well, but this is what I had to do for my old man. Honestly, some of them have changed over the course of his 17 year life, but those are the current issues I have with him.
If he's 13 weeks now and he's had diarrhea for a month, this started at 9 weeks? How old was he when you got him? Was it an issue at the shelter/breeder? What food did they have him on? If you have changed his food twice and you are not feeding him what he was before, plus a bland diet, that is a lot of switching in just a few weeks. That's o e other thought. I'd be very concerned about diarrhea in that young of a pup, so I hope it resolves!
Has the puppy been tested for Hook Worm? Our puppy's Mom was brought up from the South and most of the litter ended up with Hook Worm. It's not as common in a lot of states so some Vets don't think to check for it. She also had Coccidia which I had never even heard of, and that was what the Vet thinks was truly causing the digestive distress. They treated that with a medication called Albon which of course my puppy ended up being allergic to and then we had to treat her with an $80 medicine used in horses shipped in from Texas. A couple days in to treatment and the diarrhea stopped.