I would be honest with her, but try not to do it in a "mean" way, which is the tricky part. Let her down gently. Maybe she could say something like "I appreciate that you want to be friends, but I'm very busy and don't have time to hang out," or something like that. It's possible that the "weird" lady is autistic or neurodivergent (ND). We tend to have trouble reading social cues, and that may be the case with this woman based on how you described her. /srs
Gotta draw a clear line that you're only classmates - hopefully they haven't traded numbers or anything like that, never agree to hang out socially, keep talk related only to the course and maybe a little small talk (keep details about her life out of it), if she has to be a little short with her, so be it
I am not acquainted with the culture so maybe I'm totally wrong. But a "loud" person who wants to befriend seems to be a person who dominates a social interaction. Some people try to boss you into being their friend. Be polite but not soft. Do not follow invitations, do not invite. Do not let that person come close to your personal sphere. But be polite. Make it clear by your actions that a closer relationship is not supported and wanted. But do not express dislike in harsher terms. "Loud" people lose interest when they face resistance that is non aggressive. They press and push to gain a dominant position and love to show behaviour close to soft-bullying when they find a friendly behaving person they think they can command. Be adamant but not in unfriendly terms. Some "loud" people can show some verbal aggression and be even more loud when they see their will isn't followed. They usually are not shy to touch and grab you physically which makes many people uneasy and unhappy. In such a case do not let you be pushed around verbally or physically. Make it clear that that is not friendly and not acceptable. But keep it on the non aggressive side.
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