You seem to have trouble killing your opponent. On the second stock after your uair, don't do any fancy shenanigans if your opponent isn't dead yet; you could've gotten an easy KO by simply following up with another uair or a bair. Polish up on tech skill, since somtimes you airdodge for no apparent reason, don't cancel your shine, etc.
It's not always the smartest thing to go for a shinespike, sometimes chainthrowing or just simple uthrow to usmash is better, since you can pretty much 0-death Fox/Falco just by chainthrow, which eventually leads to a bair/nair and a simple edgeguard. Dsmash > shine if you position it so that they are unable to tech after getting hit by the dsmash, since the hitbox is quite large.
If you're going to double jump, make sure to fastfall so you don't spend too much time in the air, since that's where you're pretty vulnerable. In general, just try to speed up your Fox, flow from one movement to another, so as to leave as few openings as possible.