I do not have research though and I do not know how much this will hurt my chances. Does anyone have any advice on how to go about finding someone to work with? And how much this will affect my application next year?
I started researching at the start my junior year, too. My school has a list of profs online willing to mentor and I emailed one to set up an interview. If your school doesn't have this type of list, try looking up the profs in the bio dept (or whatever you're interested in). Their webpage profile usually lists their research interests and you can email the ones you're interested in working for to set something up.
Don't worry about your app, I think a year is decent for most schools especially if you don't plan on applying to a really research-heavy med school.