I have recently (a little over month ago) adopted a dog from a shelter. He is year and a half old mutt, looking a little terrier - like, shaggy and wirehaired. He was at the shelter for half a year and he went for a walk there once a week. No one knows what was his story before that time. He is not trained at all (I actually found a "dog school", that we will start going to in a month), but when we go for a walk he looks if I am still behind him and stops to wait for me if he outruns me. In general, he comes when I call him (most of the time) and "checks on me", when he plays with other dogs (which he loves).
He loves to run and if he doesn't run enough he gets bored quickly and destroys stuff at home or moves them to the middle of the room. When I am at home, he nibbles lightly on my hands or legs and licks my face and tries to stand on me (he gets quite needy and active). That is why I started to let him off the leash pretty quickly after I got him.
But recently I have noticed that he gets crazy around small dogs (he reaches my knee and is very slim, but weighs 15 kg, so he can be considered medium sized I think), especially if they are on the leash. He starts to jump and barks at them and even though he is not aggressive and honestly looks like he wants to play with them, he scares the heck out of the dogs (who, to be honest, sometimes start barking first and do not look too friendly while at it, but he's bigger so it can look alarming) and their owners. At the same time he want let me touch him and won't come if I call him - he's lost in the moment. Afterwards he once got diarrhoea, though it could be caused by the fact that the dog owner we met was pretty drunk.
How can I help this situation and calm him down? Or exercise without letting him off the leash? I started to keep him on a leash, but even though we walk for at least 2-3 hours daily, he seems not exercised enough. I would also note that I am currently not fit enough to run with him as much as he wants so I need quick and creative fix to make the situation better while I am getting fitter. I don't want people and their pets to avoid us like plague, since he loves playing with other dogs and most of the time does so beautifully.