No chlorine present after winter

It's been a rough New England winter. My above ground pool cover didn't hold up so well with the elements. It never came off completely but came pretty close and I got some decent sized tears in it. I basically kept adjusting it and patching the cover best I could. Now that the ice has thawed out, I've been pumping water out because it's been too high. Today I decided to take a reading and it doesn't look to good even though I brought it to shock level when closing. I imagine it's because of all the rain, and water I've been pumping out. I wasn't planning on opening up the pool until mid May but maybe I should do it sooner? I don't know if putting liquid chlorine (I use the BBB method) without any circulation is a good idea. Should I pull back the winter cover and try to mix it around manually with my leaf skimmer (which will be a slight pain in the arse), or just leave it be until I'm ready to open it? The water still looks clear, but it kind of smells like a dirty fish tank. Anyway, looking for suggestions.

FC: 0
CC: 0
ph: 7.0-7.1 ish
CYA: less than 20

If it were my pool, I'd get some chlorine in there. You can use a submersible sump pump if you have one to circulate. If not, use a broom or something and just do the best you can. You also need to keep an eye on that pH. You don't want it to go below 7.0 because readings lower than that are acidic and can damage your pool. If you don't want to mess with the chlorine now, then don't. If it turns green, you can always get it cleaned up. Its up to you but like I said, if it were mine, I'd get some bleach in it. (I already have my pool and equipment hooked up and am chlorinating. If I don't it will start turning green pretty early in the spring as we got hot pretty early. It was mid 80s today.)