Is my main feed the correct size for my panel?
Yes, you should immediately downbreaker to a 135A breaker. Hold on. Those aren't made. 

Oh dear.  Well, per NEC  240.4(B)(2), you should round up to the next available breaker size. 

You'll need to fit a 150A breaker ASAP.  Sorry to put you to the expense! :) 

Seriously, there's  one other thing that may apply here.   Since all the power for the entire domicile comes through this feeder cable, it actually gets to be derated like a service.  Per 310.15(B)(7), you apply a (favorable) 83% derate, meaning the 150A breaker only needs wire rated for 124.5 amps.  

Alternately, take your 135A wire ampacity and divide by 0.83 to give 162.7A if it's handling all the power for a domicile.  That again rounds up to 165, 170 or 175A depending on which breaker sizes are actually made.