Some are just opinions, so take with a grain of salt.
Too much Uthrow. It only tends to work when people don't know how to deal with it unless you are putting them on a platform. Dthrow is much more reliable. Also, after 30% or so, try putting in a pummel, maybe two are higher percents. It can help speed up the damage racking, which is especially useful against spacies who will cc everything for ages, making those grabs vital.
Your movement didn't seem like it had a specific goal. It wasn't staying in falcon awkward ranges to put pressure on, or really baiting a miss. It just seemed unpredictable for the sake of being so. As such, a lot of your openings came from the falcon making mistake in your face, as opposed to you working for an opening. You also threw out a lot of badly spaced tilts which a better falcon may have punished you more heavily for.
For some of the edge guards, you just needed to stay on the edge. For others, you need to remember that Dsmash is pretty good against falcon, and a run up Dsmash could have been a really good option in a few circumstances. Additionally, when you forced him onto stage, you seemed to just fair him almost every time. Unless he's at stupid percents, all that is going to do is add 12% or so and let him reset.
Instead, try to either just stand, grab pummel, Bthrow or ledge hop a uair/dair to set up a bair/ reverse fair to put them off stage again.
Generally though, it was pretty good. You played the match up and didn't jump around like crazy, giving falcon openings to use his amazing uair on you.