Can a junior apply for internships during winter break?

Hey guys, I'm new to this thread, but if you could help me out here it would be much appreciated!

So I'm a rising junior in an ivy league school majoring in econ who is kinda screwed. I've had one leadership internship that is unrelated to finance and my ECs are decent, although this upcoming semester I want to be a part of more finance ones. The problem is my gpa, which is 2.95. It's terrible and there's no way recruiters would even entertain the thought of hiring me, regardless of how charming I am.

However, with enough hard work I can drive it up to 3.1 by the end of the semester. I know it's not a BB gpa but considering the vast potential improvement, it could be a good look.

This brings me to the main point, would it be viable to apply to a boutique or some smaller internship after the semester ends and eventually work up to something bigger in the long run?

Thanks for your time!

Btw I'm interested in both IB and consulting.