I've been taking an ASL class for nearly three years now and although I wouldn't consider myself fluent, I might know things that could help you.
ASL isn't perfect English. It is its own language with its own rules. Don't let this discourage you though. ASL is fairly easy to understand. I've heard the joke many times before that ASL sounds like Yoda if you literally translate everything in English and I think this is pretty accurate to a degree.
I wouldn't say you need to be fluent in order to write a deaf character though. Knowing someone who can help you (like a Deaf person or an ASL teacher), but it's not like you need to draw the whole sentence each time your character speaks (your hand would surely hurt after a while!)
Here are some cartoons and comics that use ASL:

(I recommend this comic, it's pretty funny on its own so you don't have to know a lot about ASL to enjoy it- but it's got a bunch of bonuses for Deaf people/people who know ASL)


And this isn't even all of them!
I'd say-
1. Familiarize yourself with the language a little bit. You don't have to study it for three years or anything, but at least know some basics.
2. Having a character who knows ASL means that you can't hide their hands when they need to speak. If you hate drawing hands as much as I do, this sounds like a nightmare. Fill up a page or two with hands and then pick some signs off the internet to try to replicate. There are plenty of educational ASL drawings of signs you may need. (Some might even have full sentences!)
3. Being at least a little knowledgeable about Deaf culture might help as well. Deaf people are usually very proud of their deafness and there's a lot of things I don't find myself qualified enough to explain. Searching on the Internet for Deaf people or finding a Deaf social media website would be great for research!
That's all I can think of right now, but I hope this is useful!