How do I find the input resistance for this circuit. I think it should be infinite but not able to analyse properly. Thanks.
If \$(1+RG) \neq 0\$, then the current is zero and so the input impedance in infinite. Otherwise the circuit doesn't have a unique solution.
To see this, note that \$i = -GV_x\$, where \$i\$ is the current entering the device. Since \$V_x = R i \$, this gives \$i = -GRi\$ or \$(1+RG) i = 0\$.
The voltage drop across the transconductance source is indeterminate since it is a current source. In reality there is some amount of shunt resistance across it, since true Norton sources do not exist. Re-do your Kirchoff analysis with a Norton resistor and solve for Rin. Then take the limit as Rin approaches infinity. If Rin becomes infinite, your initial analysis was correct.