To answer your question, yes, your switching from a DE filter that you probably regularly cleaned with pool water that caused dilution to a cartridge filter where you no longer remove pool water and refill with fresh is one key factor in your situation.
By no longer regularly diluting your pool water, the Cyanuric Acid (CYA) levels built up over time. You were probably using Trichlor tabs and for every 1 ppm Free Chlorine (FC) you add to your pool with such tabs, you also add 0.6 ppm CYA. The problem is that whereas the chlorine gets used up, the CYA does not and continues to build up unless you regularly have a lot of splash-out, backwash, drain/refill or other dilution of the pool water.
First you need to get rid of the algae in your pool and that will not be easy to do with chlorine alone given your high CYA level. Even if you did clear your current algae bloom, you would need to maintain an FC level of at least a minimum of 7 ppm in order to prevent algae. If you instead do a partial drain/refill of your pool to get your CYA level to 50 ppm, then you would only need a minimum FC level of 3.7 ppm. With a more normal CYA level of 30 ppm, you only need a minimum FC level of 2.2 ppm.
To prevent the buildup of CYA, you have several options. One is to switch to using bleach or chlorinating liquid as your source of chlorine. You could also use Cal-Hypo instead, but that will build up Calcium Hardness (CH) over time. For every 1 ppm of FC from Cal-Hypo you increase CH by 0.7 ppm as well.
Another option is to use Trichlor but also use a weekly maintenance dose of PolyQuat 60 algaecide. This can get expensive, but it will keep the algae away and is what most pool chemical manufacturers recommend in various "programs" of theirs. Sell you Trichlor with CYA in it, have it build up and require you to use an algaecide that they also happen to sell. You can keep a lower FC level with the algaecide -- probably around 3 ppm will do, but when the CYA gets far above 100 ppm then there are other problems to deal with (very high CYA levels may damage plaster/gunite).
You can, of course, regularly do a partial drain/refill to keep your CYA levels in check when using Trichlor.
Regardless of the option that you choose, you should invest in a good test kit such as the Taylor K-2006 kit you can get at the following links (and at some pool stores, but be careful since the K-2005 that some pool stores carry is not the same and cannot measure high chlorine levels accurately).