If you join a chapter and initiate at school #1, you will become an alumna when you leave. Upon arrival at school #2, if they have a chapter of your sorority, you are eligible to affiliate. By eligible, I mean it is possible, not an absolute instant guarantee.
Assuming you're a member in good standing, you'll notify the new chapter and they'll let you know where to go from there. Policies vary by sorority and by chapter, but generally, you'll hang out with your sisters a bit. You'll get to know them, they'll get to know you, you'll decide if you want to affiliate, and the chapter will vote on you.
Some chapters do not accept transfers at all. These are in the minority, and are generally "top tier" chapters at schools where Greek Life is a big deal.
Some chapters have a lengthy and formal process akin to a second recruitment, where they have a lot of prospective transfers.
LoveinZTA told her story about transferring from Baylor to Texas. Also in the minority, also common at competitive chapters at big Greek schools, especially flagship state Universities.
Make sure you want to affiliate with your new chapter. They might be completely different than your chapter of initiation and unlike what you are looking for in a sorority. If you affiliate, you don't get a chance to change your mind and go early alum before graduating if you decide you don't like them. You'll be financially bound the rest of college.
Some questions/things to think about
:
Why are you planning to transfer if you know you might end up staying?
As to how hard it is to get a bid as a sophomore, your chances don't get better the longer you wait (unless there were drastic changes). I don't know anything about your current school, so I can't comment on that.
If you do transfer, you might not fit with the chapter at your new school (whether that is your perception, theirs, or mutual). Would you be ok with having one year of collegiate activity and then alumnae status?
If you wait until you are a junior and go through recruitment at your new school, you are more likely to find a good fit---if chapters at your new school are friendly to junior PNMs. In this scenario, you have more of a risk of not being Greek at all. Would you be ok with that?
If you get a bid at school #1
and don't initiate, you are a "free agent" at your new school. You are not bound to the sorority you pledged, and they are not obligated to take you.
Also, it's probably too late now, but if your housing spot could be filled, is there a way you could have gotten out of it? I.e. if you found someone personally to fill it.