No increasing the transmit power does not mean the data rate increases. However, if you wish to transmit at higher speed then you do need to increase the transmit power.
Changing the amplitude does not increase the data rate, unless you are using an amplitude based modulation scheme to represent data bits (such as QAM - quadrature amplitude modulation) and you change the design and use more levels to enable more bits to be transmitted.
You need to understand what the modulation scheme employed is. Bandwidth can change (and often does) increase with increased data rate.
Once you understand what modulation scheme will be used, then you can lookup in published articles how to calculate the bandwidth for a given data rate. It is not necessarily trivial.
I'd advise: forget Shannon for the moment, that enables you to calculate the maximum information carrying capacity but it seems if you yet don't understand the terminology, definitions and relationships between bandwidth, power, data rate.