Urinating quickly after drinking water.

I feel the urge to urinate quickly in less than half an hour after drinking water. Frequency of urination increases when the weather is a bit cold. I feel.like body not absorbing water and whatever I drink is converted to urine quickly. After urination, I feel.thirsty again and drink water and the cycle continues. Also my bladder is not emptied fully after urination and I have to go few times again. Test results are normal except mild prostate enlargement (BPH) for which I am taking medication. I am not sure what other tests are needed for this problem. why my body is rejecting water so quickly after drinking?. Why do I feel.like my body not absorbing water?. What could be the cause for this problem? I am worried if this problem puts more load on kidneys and damage them. Please advise.