Speaking from experience, there are plenty of D1 and D2 schools that will take you in happily, depending on how you have been training in high school. Especially at the D2 level. Being a D2 runner, I have experienced that mostly all the teams except those at the very top of the chain (Adams, Metro, Mines, Grand Valley) will allow walk ons the chance to train for the summer and try and come in and make the team.
Myself, I was worse than you in high school, with PRs of 800 - 208, 1600 - 5:01, 5k - 18:33. The coach of the team at the school I now run for saw that I was enthusiastic about running and that my training in high school was pretty lackluster so he gave me a shot to walk in. The program is a mid-level D2 program so while it wasn't a championship caliber team, it was a regionally competitive one.
My freshman year of cross was way rough. The mileage I was trying to do took it's toll on me, and my PR was 32:01 before getting cut. However, I used this as a rally point and continued to train, focusing on track and what I thought was my strong suit, middle-distance running (my 2:08 was my best HS time comparatively to the other distances, and I had run a 54.1 400).
I trained with some friends and worked my ass off on the track and in the weight room and was able to snag a spot on the track roster. Started off my indoor season with a 2:07 800 and dropped that time every meet in succession until I ran a 1:58.5 my last meet in outdoor and qualified for our conference meet.
From there, my career has been sealed. I've never been much of a threat in cross (PR of 27:18, consistently running in the high 27's, low 28's), but my training has paid off on the track where I've significantly lowered all of my PRs and just narrowly missed provisionally qualifying for nationals in the 800. My PRs are now 800 - 1:54.1, 1500 - 4:07, Mile: 4:24.6, 5k - 16:28, and like previously mentioned, I am still amazed at some of the workouts times I've run compared to what I ran in high school.
So pick a school, talk to the coach and tell him you really want to give it a shot, and as long as it's not a top level program, you should be at least given a chance to train and walk on. From there, just keep working hard and it will pay off eventually.