Hi Yellowz,
First of all, probably it's possible to get sub 20 with all the algorithms you know now. You are probably spending most of your time looking for pieces and patterns.
Yes, I do think learned algorithms help. In general, there's not 1 algorithm for each case, it helps to know more than 1 solution for one case, it helps doing things from multiple angles and sometimes canceling out moves. So do keep an eye out for extra algs, especially for cases you hate.
Other tips that might help:
1. Solve the cube slowly, and count the moves. As a beginner, you want to try to minimize the move count. Move count isn't everything, but it will help to know efficient solutions. Always keep looking for shortcuts. You can find a lot of F2L algs and shortcuts yourself. If you find one yourself, chances are you'll remember it better then when you learned it from a website.
2. Try to stop for a moment after the cross, and plan the solution for 2 F2L pairs. This also works best without a timer. This can improve lookahead. Planning and looking ahead helps to pick the easier pair and cut cube rotations. I said 'without timer' because you want to give your mind time to learn this. That's very difficult under time pressure.
3. Practice inspection and execution of Cross+1 pair (x-cross). Measure the execution with a timer, and try to beat your avg record for that 1 step. Try to plan the entire solution (of the x-cross) during inspection. Don't limit inspection to 15s. Just give yourself time. Your mind will get trained to look further into the solve during inspection.
4. Keep watching fast cubers for inspiration. I always felt that it helps. I am not sure how.
5. Find racing partners, to practice solving under pressure.
6. I don't know if you are color neutral, but if you are not, I'd suggest you give it try. When I started cubing, I could win comps without it, and I am now handicapped because I am not color neutral. I am trying to work on it, but not sure if I can ever become CN. Starting with a rubbish cross because you are not color neutral is... Stupid. If you get comfortable starting with any color, you can often benefit from an easy start, and you'll rarely have a very bad cross situation.
7. Enjoy being a newbie. You can still beat your record frequently, make sure you enjoy it!
I hope that helps, good luck!