i think its a completely normal thing and doesn't serve as any indication of being overly sensitive. you're just establishing a personal boundary regarding comfort and a way of speaking. some people like to tease friends and others may be the type to play fight or hit but if its something that makes you uncomfortable you're allowed to say that you prefer to be left out of that kind of joking and instead prefer something else and a good friend will honor and respect that boundary
for me with work friends the established boundaries are those typical of a formal work setting so there's not a whole lot of physical contact other than maybe polite hugs or a handshake but i know that even in high school or middle school with my friends we were all fine with laying out what we were or weren't comfortable with and had no issue respecting those boundaries. its the basis of building healthy relationships and helps make you a stonger communicator.
granted there will always be folks who dont care to acknowledge or respect boundaries but there's ways to go about navigating that as well.
but happy birthday when it gets here 