Get a second opinion, and get it from someone local. I am not a big fan of online mortgage professionals. Buying a home is probably the biggest purchase you will make in your life. I don't know about you, but I'd like to be able to walk in to the office of my loa officer and shake their hand.
I always advise my clients to shop around for a mortgage. You want to know what the interest rate will be, approximately, what fees you will be asked to pay, are there any 'points' (ask them to explain that to you as well) and what your monthly payment will be and whether those payments will ever increase. You should receive a 'Truth in Lending" statement. Put the three estimates side by side and choose the one that is best, over all, for you.
I also recommend talking to local, mortgage bankers. I do not mean big banks, but small, local companies that specialize in writing mortgages. If you don't know any local mortgage bankers, contact a realtor and ask to be referred. Realtors are here to help people like you purchase homes. They will know who is easiest to deal with, who has the best rates and who can get the job done. They will be happy to help you find a lender in hopes that, if you do qualify, you will allow the to help you find the home of your dreams.
Having said that, USDA loans are zero money down and your credit scores are pretty good. The amount you may qualify for is based on your income and debt to income ratio. So, yes it does sound as if you could qualify for the loan.