Dress too tight in bust - advice?

I found a dress I absolutely love that was on clearance for more than half off. A 1400 dollar dress for 499. When I tried it on, I thought it fit almost perfectly. I tried it on without a bra, and didn’t think about the fact that when I add a bra, the dress will fit differently (duh...) I was just in love and so happy I found that deal.
i tried the dress on with a bra and although it still zips, it is very very tight around the bust, mostly in the back. It’s almost like I can’t pull the dress up enough when it’s fully zipped, and it’s sitting lower than it should because my measurements are obviously smaller below my bust.
i can’t get an appointment for alterations until March, and I’m freaking out about what can be done to make the dress fit. It’s such a marginal amount it would need to be “let out”, prob less than an inch. Would they need to make it a corset back? What else can be done?
i don’t think losing weight will make a difference as it’s the measurement of my bust and ribcage, and I don’t really want to lose weight from my bust. I’m pretty lean as it is and don’t want to lose more than 4lbs max before the wedding.
has anyone had a similar experience?