Fish do indeed have arms, or at least the homologous structures (pectoral fins). They rely on these to provide lift at the front end of the body. Unlike T rex they don’t have huge heads, and their bodies are streamlined for movement in water, which is not true of terrestrial tetrapods like T rex.
Fully aquatic tetrapods, like whales and seals, do indeed swim with their tail/hind legs. They are also highly streamlined and they also basically lack a neck, and still retain powerful forelimbs for braking, steering, and adding lift if necessary. Streamlining is extremely important in the dense medium of water, and this issue gets increasingly important with large size, as per T rex. A tadpole can get away with a lot just because it’s small.
The tail of T rex does indeed balance the weight of the head ---- in fact there is some reasonable speculation that the arms are so small because the head is so huge. But that balancing is done by cantilevering the body over the legs in air. In water, the head would sink, as shown in the reconstruction of a swimming T rex. Which isn’t to say it mightn’t be able to paddle for some short periods, but it would have a hard time getting its head above water, if it could manage it at all.
The boy swimming without arms is doing so on his back. This would not be an option for a quadruped like T rex as it would be unable to straighten the legs at the hip to align with the body and they would stick out of the water. Not a viable option for swimming.
All terrestrial tetrapods that are reasonably adept at swimming use their forelimbs to generate lift at the front end so that the head doesn’t sink (and also to generate thrust for propulsion). For example, most likely Spinosaurus.
(Phylogenetic bracketing won’t help here, especially as swimming is done in very different ways in birds and crocodiles [and also in different ways in those few birds that do swim], but functional morphology will. Depending on how one drew the cladogram, phylogenetic bracketing might inform us that humans knuckle-walked, but functional morphology would show that we did not.)
Having tiny arms would be a huge impediment to T rex attempting to swim. It is not an animal that is “designed” to swim, and it is highly unlikely that it was able to to any great extent. SGI footage is not evidence. I stand by my original “intuition”. It’s not “I just sorta feel”, it’s based in knowledge of vertebrate functional anatomy.