Hola Luis, 

Here is a list of swimming pools in Geneva and surrounding area

https://www.cagi.ch/en/culture-leisure/swimming-in-geneva-and-the-region/

Probably the cheapest swimming lessons will be in Annemasse, where they have a very nice pool complex called Chateau Bleu. 

Buena suerte!

I'll just tell you what I found when I was doing my research, you'll decide what works for you

ENG natation ecole at Vernets pool offer 5 group lessons for 130chf, and 5 individual lessons for 260chf

GN1885 offfer 2 lessons of 45 minutes each for 55chf

My coach for swim offers 30min private lessons for 50chf

another way is to search for a swimming pool, and they will most likely have instructures on their page (perhaps a community pool close to where you stay) I took a lesson at Carouge piscine for 40chf, 30min, a private lesson, they will allocate you an instructor who speaks English if they have one. For the group courses, they are mostly in French.

Good luck!

thank you