What is the volume of the pool?
What type of pump and filter do you have?

Test strips are generally not reliable but they are better than nothing. You must very carefully "read" the FC and pH levels. CH, T/A are nearly hopeless, and, if your strips have a CYA (stabilizer) level, it's totally hopeless. If all you have are strips, you can take a sample to a pool store and have them do their free test on it.

However, they will attempt to sell you chlorine tabs, calcium increasers, total alkalinity increasers, pH Up!, Low'n'Slo, clarifiers, algaecides and...phosphate reducers. You could get a VERY hard sell--be strong!

The only thing you MAY want to buy for now is liquid chlorine--10-12.5% (double-strength bleach). If your CYA is low or zero (likely given the vegetation), you'll need some of that--the roughly two pound container is all for now.

Depending on the store, they may push hard, they may back off, but I wouldn't buy anything but liquid chlorine and stabilizer (the latter ONLY if CYA is low, 0 to 25).

When you say you don't use chlorine I'm confused. You'll need to start to using chlorine if you want to clean the pool.

You will need lots of chlorine. Best would probably be bleach or liquid chlorine. We need to see test results.

Meantime, there's a better kind of skimmer for your problem called a "leaf rake" that has a VERY deep net and a squeegee edge that's ideal for scraping the bottom and is safe on vinyl. "Leaf Rakes" aren't as good for surface skimming as regular skimmers but are far better for the bottom.

There is also an inexpensive garden hose-driven vacuum that has a bag that is very good for leaves and such. A few brands are out there. There are variations like the "universal leaf gulper" that run about $25 (you said funds are limited) and "Big Sucker Leaf Vacuum w/ Brushes" that's about $20. There's a "Black Magic" vacuum (<$20), a "Blue Magic" for $10, etc.

Just Google "pool vacuum heads"