Tony,
Welcome to BP and to San Antonio. I would definitely agree with the folks above who cautioned you about spreading yourself to thin. I'm sure you could get approved and I'm the guy who cringes when I hear loan officers talking about how they could get anyone approved.
That being said, I don't know your situation but there are million ways to make more money the side and/or reduce expenses between now and July. I moved out of my house a few months ago and now rent a room from a friend so that I could lower my expenses and make that house a short term rental. Its not the most desirable situation but I took a house costing me 1300 a month that now makes me well over 1300 a month after it pays my mortgage. There are also things like uber and other odd jobs you could do to increase your pay between now and then.
You have options, and its a pretty good spot to be in when you already have a cash flowing rental and are trying to figure out how to get the next. Good luck man, let me know if I can help!