Home purchasing after refinance and invsmt property purchase

Hello BP. My wife and I recently refinanced our investment home in California, did a Cash out Refi on our primary home, and used that cash to purchase an out of state rental home. All within 2 months. I have the option to use my VA loan and want to start looking to find a new primary residence and use our current home as a rental as well. My broker told me that we would have to wait 5-6 months before getting pre-approved and purchasing a new primary residence because the lender wont like all the action thats been going on. Is that accurate? Because of all the refinances and investment purchase, does that prevent us from looking for a new home this soon? if so, why? we would like to pull the trigger and buy now because the market is just insane here in california. Thanks for any advice!