can i give my character a curse?

i was wondering, because i recently made a Tiefling dnd character and i wanted them to have a curse. they're backstory is basically that they got a curse from something. i wanted that curse to be so that my character cannot have their skin touch direct sunlight, since i thought that would be a cool concept and i could play around with my character's clothing designs. this also leads my characters reason as to why they wanted to join the adventure, like the campaign. to find like a cure and get money after loosing their job. i am kinda new to dnd, not familiar with everything, but i have played it for like about 2-3 years and i am comfortable with having more complicated characters, but i am not completely sure on this aspect. is it possible for my character to have this curse? if so does it exist somewhere? are there rules to the curse? if such a curse doesn't exist am i allowed to just make one up? if i am allowed to do that is there some sort of disadvantage i should add? 

(chat i swear this is my first time using like dnd beyond for game rules or tips? i posted this in tips and tactics first and then realized maybe this question was in the wrong category? i have no idea how to delete threads, or if thats even possible, so yeah my bad if you see this in both...)

This is an ask your DM situation because it’s pure homebrew. I might allow it, personally, but that doesn’t matter at your table. You just want to do it in a way that doesn’t end up dominating the adventure and making you a main character.

But if a player were to come to me with this, my first question would be what happens if you do get in sunlight? There used to be some species that had a trait called sunlight sensitivity which gave them disadvantage when they were in bright light, but they had more to do with being underground dwellers not used to such bright light. I’d probably suggest something like that. It’s simple, tangible, you track it yourself, and it won’t eat into table time much. 

I’d also want to know why you were cursed, and if removing that curse is a personal goal for your character. It could make for a decent motivation to go adventuring and be interesting. 

D&D doesn't have a disadvantage system other than 2014 flaws (which were just arbitrary values), but you can simply roleplay them being cursed and unwilling to let sunlight touch their skin without assigning any particular game mechanics, which is what I'd probably recommend, as major effects would likely be disruptive for the game. Other than that, I'd still check with the DM -- it's a perfectly fine backstory element that could be interesting, but it also might be something that they don't want to deal with or doesn't fit with the campaign.

Not with much detail, but in Chapter 3: DM’s Toolbox from the 5.5e DMG, section Curses, there is something about "Narrative Curses".

It mentions, for example, what Xalthu said about why you were cursed and how to end it.