There's a lot here... your age is a determining factor for starters; i.e., the older you are the harder it will be to make the kinds of physiological changes that you need to make very quickly in order to meet your goal in 77 days.
200s are not comfortable events when swum hard... you have to swim them like almost all-out sprints, but the distance is too long to be able to maintain your all-out sprint speed, so technique is really important, turns are really important. The training for middle distance is about making your body more comfortable with the uncomfortable (which will make ever faster paces seem comfortable).
All the weightlifting in the world is not going to help you swim faster if you don't simultaneously work on technique, swimming efficiency, feel for the water... all of which you can only really get from swimming. In fact, weightlifting could actually slow you down if you don't do the right exercises, the right way. Lots of drills in the pool will help you more with technique.
To be able to swim a 200 fast, you have to be able to swim longer than 200 at a normal pace without getting tired. To be able to swim 200 in 2:45 you have to average about :41 per 50, so your absolute max speed to something faster than :41. Swim some 300s, 400s, 500s at slower speeds if you can maintain technique (this will improve your endurance); then swim a lot of hard 25s and 50s to try to get your top speed faster... swim 100s and 200s to bridge the gap between your aerobic pace (the longer stuff) and your sprint pace (the short stuff)... this is your anaerobic zone, where your 200 lives, teaching your body to deal with ever increasing levels of lactic acid; push your threshold back farther and farther. But mix it up, get in the pool as often as possible, increase yardage slowly, take an easy day after a really hard day to let your body recover and rebuild... then attack it again.
And have someone look at your stroke, maybe find someone to swim with, you'll swim faster with someone else pushing you.