2 weeks ago I could barely run 0.24 miles, not even 3 minutes and I was tired. Today I ran 1.02 miles in 14:26 minutes. Will I be able to run 1.5 miles in under 16:10 minutes within a few months to join the Navy at my rate?
16:10 comes out to a little under an 11 minute per mile pace. To be safe, you should aim for a 10 minute per mile pace. Every week or so you should run that pace as long as you can, using a fit bit or a running app or something to make sure you're keeping that pace. Basically, your body, and you, needs to learn how fast fast enough is.
Otherwise, keep doing what you're doing, and don't forget your pushups and sit ups, too.