green pool already, help on how to handle it

Well the wonderful warm winter we have had has caused me to start having an algae bloom. I never checked the chemical levels over the winter as i usually have no issues till spring time. Im not sure how to handle it as all my pumps and lines are winterized still. I did put a small pump in and put a lot of 73% shock dissolved in a bucket to try to clean it up but it seemed to only clean around the pump. I dont feel much will help unless i remove the mesh safety cover and scrub it while i shock it. I usually dont open till maybe middle of may.
Wondering if maybe a healthy dose of algaecide may help slow it down or minimize it. I was also thinking of getting a solid tarp and putting it over the safety cover to help block sunlight and maybe slow algae growth down till i open.
suggestions welcomed. Its early to remove the cover for good as its still cold here in the nights and no way near swim weather yet. I doubt it will be below freezing much anymore here but its still possible so i am hesitant to open the pool filter and lines up till maybe mid to late march.
I want to try to slow down or take care of this algae now as i know it will worsen as the weather does warm and the water temp climbs.

If you don't want to open yet, you can just pour bleach/liquid chlorine straight into the pool around the perimeter. I do this all the time (not yet, my pool is till covered in snow and ice). Not knowing what size your pool is I cannot tell you how much, but I usually use one 121 oz bottle of 8.25% bleach at a time, I walk around the pool as it pours out. Check the next day. If water is not clear than I use another bottle, and 2 is usually all I need before the pool is clear, though the bottom and sides might still be dirty.

Sorry for your troubles.

Algaecide really won't help once you have algae; it is a preventative. Throwing in bleach now isn't going to do much but be an expense.

Until you feel comfortable opening up the plumbing so you can eradicate the algae, you can try a solid tarp over your mesh to try and slow the growth. It can't hurt.