Hi,
I can't stress thos enough, but going to confrences or anything of that sort will prove a whole lot more successful than cold emailing.
Now I'm not saying cold emailing doesn't work, it does in some cases and even has some benefits over this method (Not limited to location), but meeting a professor in person increases your chance of getting an internship by 100%.
You leave a stronger impression as they get to actually meet you and interact with you rather than you just being one of the hundreds of faceless students emailing them everyday. This is especially important for professions (e.g. Medical, Eng, Aero, Chem, etc.) where lots of students are seeking out these oppertunities.
The best part is that as soon as you get one professor that you keep in contact with they refer you to other professors, as professors are much more likely to answer emails from others professors associated with a organization. For example, I had this education professor I met at a science fair which refered me to 2 aerospace profesors, one of which I secured a full lab internship from.
I have met so many professors through this method, including a edu. prof., Harvard/Columbia professor, 1 environmental eng., 2 NASA aerospace eng. professors, and a multitude of grad. students.
Of course cold mailing still works wonders, but I thought to share this alternative method that proved more successful in my experience!
Good luck on yall's lab internship journey!!! (Even if you don't get one, researching independently works awesome too! That's what i did last year which I think also helped with my credibility.)