My OPT ends in a few months - am I still in time?

Usually yes - if your OPT ends two or more months from now, you have a comfortable runway. Typical rhythm: admission 1-2 weeks after a complete application, then the SEVIS transfer, then the new school issues your I-20 and CPT in about 1-2 weeks. Give me the exact date on your OPT card and I'll map it backwards for you.