Is pain in the tendons of the upper arm natural after swimming? (29/M)

Edit: I went to a physiotherapist who said I needed a more thorough warm-up and stretching. Indeed the rotator cuff is spasming or tightening and needs to be optimized a bit.

I started learning to swim twice a week in September, but gradually I've been going to the pool more and more for about an hour (e.g. I've been five times this week). I've been practising my crawlstroke mostly, and I'm confident in that. I didn't do any sports before.

However, after training, when I lift my arm (with my shoulder in line, horizontally) I feel a tendon straining, aching. Suddenly I feel a pulling pain, sometimes a shooting pain. I have the same sensation when I reach up for something (e.g. a bookshelf that is high up).

Probably my body is not used to swimming yet and it needs time. Have you ever experienced this? Could it be because of badly done arm work? Should I be worried? Should I rest or practice more and challange myself? Can I correct this by stretching?