Hi Heather...Welcome to the forums and to the Planted tank forum
Right off the top you are going to find that the relationship between algae, plants, light etc. is not a casual one paragraph post. I would encourage you to do some reading in the forum and ask questions about what is unclear.
You are also going to make a decision on what type of planted tank you have.
A tank with a few plants low tech
or
A planted tank High tech
There are some major differences in how you manage each type.
The Chemicals...
Both products you mentioned will kill everything in your tank. If not sooner, than down the road a bit.

I know what it says on the label but your plants will suffer and some will never flourish.
Some Quick Help with the algae.
A 72 hour complete blackout of your tank (NO LIGHT) will kill the algae. The nuisance green algae you have has no way to store energy from light and will die if deprived for 72 hours.
Do a search on blackout and read the threads.
What you will learn is that you need to address the root cause of the algae outbreak. Amount of light, overfeeding,
water quality, overall health of the plants etc.
You could post a complete set of tank parameters to help us understand what is going on in your tank. There is a sticky post at the top of the forum that will be helpful.
We look forward to hearing from you
Regards,
Jay