I am going to be playing in a Castlevania-based D&D 5e game. In this world there is strong racism against elves and a general fear of magic. I want to be an elf, but I think in this world I would be inclined to try and hide that fact from my party and anyone I met. Do you have any suggestions for how to go about this before I bring it up to my DM?
The easiest thing to do, that is accessible to any character, and requires very little investment of resources, is to get proficiency in the disguise kit (probably from your background).
Disguise Kit. This pouch of cosmetics, hair dye, and small props lets you create disguises that change your physical appearance. Proficiency with this kit lets you add your proficiency bonus to any ability checks you make to create a visual disguise.
All you really need to do is hide your ears, and "disguises that change your physical appearance" sounds like it should certainly be able to do that. This is almost certainly the best option, but here are some others.
The 1st-level disguise self spell will allow you to disguise yourself as a human, and anyone can get it with the Magic Initiate feat. However, it only lasts 1 hour, so you'll probably need to be able to cast it multiple times per day.
If you can talk your DM into giving you one (good luck!) a Hat of Disguise lets you cast disguise self at will.
The 2nd-level alter self spell will also allow you to disguise yourself as a human, but will require you to be a third-level wizard or sorcerer. It also requires concentration, so there's a risk of your disguise dropping at an unfortunate moment.
As mentioned in another answer, a 2nd-level warlock has access to an invocation that allows them to cast disguise self at will, which would be great for you. A 15th-level warlock has access to an invocation which allows them to cast alter self at will, but that's not really an option unless your campaign starts at a high level and you were planning to be a warlock anyway.
A 14th-level druid of the Circle of the Moon can also cast alter self at will, and it's likewise infeasible except if you're starting at high level and planning on becoming a druid anyway.
I played a warlock with the Mask of Many Faces invocation that allows one to cast disguise self at will in order to hide my race. It was quite effective, but did require 2nd level. He also had the actor feat, which further aids impersonation.
Ear surgery aside, a magic item that disguises your character (both visually and covering any accent in speech) seems the most likely way -- plus giving the DM some hooks to hang adventures on (someone recognizes the disguise item, detects the magic, etc. and blackmails or threatens your elf, or asks for help only an elf could give; your infravision/dark vision gives you away, someone wonders why you're so slender and asks just the wrong questions -- the fun goes on and on).