Like- your body will try to avoid pain/soreness when you make your swing,
if the muscles are fatigued they will compensate.
When you want your body to do anything physical, it will do so to the best of it's ability. It will do so depending on it's physical limitations. If you are talented enough or have good enough insight into a good golf swing you can get away with more physical limitations/restrictions/weakness. If you are Ben Hogan or Tiger you can have a sore knee, restricted hips etc and still score well. They are not playing 100% of their potential but they may still have enough talent, skills etc to shoot 65.
The exact problems
you may get after bowling I don't know. Bowling may not bother another golfer but if you have a "really sore" right arm then your brain will try to figure out how you can make your swing with the least irritation to the right arm. Your brain could be avoiding pain and sending you off plane thus making the club feel heavy or maybe your arm's just pooped.
or as thefuture37 said your bowling ball is too heavy
or you bowled too many games
or you need to hit the gym
or you need the Brian of bowling instruction
![Big grin :D :D](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
Think back over the round and some pattern should emerge. There's your answer.