I feel some pressure and fatigue in my wrists and lower forearms during riding but not after it. I don't know whether it is due to weakness of my wrists or my suspicion that my 18" frame mount bike is small for my 6'1" height. But the thing is that I don't feel any fatigue after biking; only during it. What do you think the problem is?
Fatigue indicates you are using the muscle, so you will need to “check into” yourself to see how/why you are firing your forearm muscle, what task is it trying to accomplish.
Sometimes we just have some odd or peculiar habits we are unaware we are doing. For example, my wife used to complain about wrist and hand pain when riding her flat bar commute bike until I observed she held her wrists in heavy dorsiflexion when she gripped the bar. Retraining how she held flat bar grips (i.e., a wrist angle of zero) alleviated the symptoms.
Finally, as other answers indicted some component of bike fit could also be the culprit, but there is not enough information to comment on this possibility.
What do you think the problem is?
I think your bike does not fit properly. But it's impossible for anyone here to give you advice with a remote diagnosis. you should really go to your local bike shop and spend the money for a bike fit. this will really help you and clarify what the problem is.
you should take notes at the bike fit and mark your seat post height etc. so you could fit any new bike in your life for your requirements and won't have the same problems ever again because of an unfitting bike.