If your dog is using her urine to mark/protect her space, then the hypothyroidism could be the result of this stress-related behavior. Sometimes as dogs get older and/or if something changes in their environment that makes them feel more vulnerable for some reason, they'll urinate to signal a willingness to protect that space. Generally when this is the case, the dog urinates in the same few places.
With urinary tract infections the pattern is usually different. With some infections the dogs may hold the urine because its painful to urinate until they can't hold it any more. In that case, you may see a stream of urine (as they try to make it the door) and then a puddle. In other cases, any urine in the bladder causes sufficient discomfort that the dog will urinate small amounts more often. In both of these cases the pattern will be random compared to urinating for behavioral/marking reasons.
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