Might I have Cystic Fibrosis? Should I ask my doctor for a sweat test?

I'm a teenager and I want to ask my doctor for a sweat test.
I think I sound completely paranoid.

I've had digestive issues my whole life, even though i'm 17 I can remember having stomach pains and constipation or nausea and diarrhea after eating as far back as 8 years old. I also get frequent respiratory infections, during winter I get constant flu's and I've had a bout of bronchitis nearly every year. I even had to have my tonsils removed when I was 3 after having Tonsillitis for two months straight, I've also had a long list of other respiratory infections including one that was never diagnosed but nearly landed me in hospital when I was 6 or 7. Sometimes I have bouts of breathlessness after not doing anything active.

What made me even come across the possibility of maybe having CF was my hands. After a 12 minute shower my finger tips, fingers and entire palms will be so wrinkled/pruned that at times it can be sore. After I read through the other symptoms was when I thought CF could be a possible cause for both that and my other symptoms.

Am I being completely paranoid or should I get a sweat test?

Yes, but don't stop at that. More specific testing is by genetic tests - usually initially for a limited number of mutations, the most common. You need one on each Chromosome (homozygous) to be definitely CF but you could just find a mutation on one (heterozygous). You may have a rare mutation on the other - requires gene sequencing to find.
You may try Creon (an enzyme preparation) with your meals - should help if your pancreas is not working properly (as with CF)
Don't take NO from your Doctor - get tested - If you have CF it will change your life!