How do I remove a singularity that appears when I make a fit to my data?

I am trying to fit a complex algebraic function to a data set Data, which is basically a Lorentzian. The problem I am facing that while fitting there exists an infinity. Could you help me to get rid of infinity?

Since my code is more than 30000 characters (as the algebraic function is very big), I cannot post the code here, so I have put the code on google drive, which can be found here code.

I have also tried plotting the function, the function was defined as
num[Q_, k0_, F_, [Eta], [Omega], [Alpha], [Omega]0] := algebraic function
and the plotting was done as
Plot[num[17327, 3.2616, 10^-11, 3.310^8, [Omega], 1.2310^17, 20268509.9], {[Omega], 0, 20273800}, PlotRange -> Automatic]

but I am only getting half part of the plot, please see the attached image file