i am 73 and still surfing, from the age of 8 but before my father would allow me a board, I had to swim a mile>
Being a capable swimmer meant I could swim in after any wipeout, leashes had not been invented in 1958.
Leashes break, means a swim!
next 90% or more in surfing is paddling, most surfers end up with niggling shoulder injuries just from over use.
SO! Get your shoulder checked out, get a regime of treatment and develop a strength and flexibility habit that supports your shoulder, then add surfing by progressively gaining paddle ability.
You also have to be able to pop up, so capability i n push ups and burpees at a 60 year pace would be an indicator of whether you can become surf fit!
For me now regaining that level after serious health issues is quite a hard task so all I have offer holds true for me!
But it is a great thing to do persevere !

I've taken up troll hunting just for fun, instead of a rifle I'll just use a pun! 冲浪爷爷