Same exact thing happened to me a few years ago. The backstory, I was all bowling since I was 2 years old. Loved watching bowling (old ABC telecasts on Saturdays especially), bowled multiple leagues per year, and bowled in college. I never even touched a golf club during my four years at college, because all I wanted to do was bowl. I golfed in HS, mainly for fun, I was decent, maybe an 8-10 hdcp, but never really applied myself to get better.
Then I moved from MI to DC, and I remember one March day, it was our first really nice day of spring (70 and sunny). I hadn't played in about 4 years, and saw my dusty clubs in the corner. On a whim, I said to myself, "I'm going to go golfing today!", thinking it would be a one-off. I went out to a local muni and shot 77, completely changed my outlook. I said, "You can go out after not playing for 4 years and shoot +5, why don't you actually get some clubs that fit you and take a lesson or two?" I got fitted, dropped about $1K on new sticks, and took a lesson. From that point on, golf was my obsession, not bowling. 5 years later, I'm a +1 and bowling is more or less for fun. I play in state amateur qualifiers and tournaments, and I love every minute of it.
While I was golfing obsessed, I actually completely quit bowling for 3 years. I didn't even watch it on TV. I just came back this year and joined two leagues, one house and one sport/PBA. I am bowling great, thinking less, and having fun again. I am not over thinking, trying to be perfect, or ruining my day if I bowl bad. I still get upset from time to time, yes, but that's just me being competitive. But I think my new refreshed attitude has helped me enjoy bowling more, and also bowl better because I am in a better place mentally. My thought process is that I'm just going to have a few beers with friends and bowl a few games. I don't really bowl tournaments anymore, as they conflict with golf on the weekends.
My advice to you, take some time off. Maybe it's 6 months, maybe 3 years. You will know when it is time because you will start thinking about it and getting that urge to bowl again. Focus on golf for a while, it's an awesome game that provides many of the same benefits bowling gives, all while being outside and getting exercise. I've met so many great people golfing, the same that applies to bowling. Some do both. These are two sports which work excellent together, both in seasonality and technique (mental and physical). In fact, often times I will do both in the same day when I can swing it. I'll golf in a the AM and bowl league at night.
