DB,
While you aren't going to become an Outstanding PRT'er in 18 days, there are a few adjustments you could make to ensure you pass the in-prt. First, you should not have more than 30 seconds rest in between those push-up sets. Focus on form. Second, the push-ups should be PART of your workout routine (anywhere from 3-5 days a week) including your curl-ups, bench press, bent over rows, dips, and maybe some front deltoid raises and bicep curls for good measure. All working to temporary muscle failure. 18 days is a tough time frame to ensure preparedness, but you will improve (maybe just enough) if you incorporate a high level of intensity with these exercises. You never know what you're capable of when your back is against the wall.
A posteriori