I'm in France rather than Spain but I had many of the same concerns as you about starting school at 3. DS1's b'day is in October so he started in September just before his 3rd birthday and was one of the younger ones (as they go to December like you). I was concerned about having such a structured day, so many rules, too much learning, having to interact with so many kids etc.
If I were you, I would apply for the place now as it is easier to pull out later than to apply later if you change your mind.
However, to be honest I have been VERY pleasantly surprised by the whole infant school process and very very impressed by what they do. There is some learning, but it is largely done through play and there was also quite a bit of free play.
I think it would be worth going and having a good chat to the school (and ideally the teacher your child would have if possible) and really finding out what the school day actually involves. Explain that you come from a country with a totally different approach to education (and starting age) and that you need to understand how it works.
Also, here school is not compulsory until 6 and depending on the school they do allow more flexibility than I expected. In the end we put DS1 in for the mornings only for the first year, although by about March he was happy to go back for one afternoon and then I think two by the end of that school year.
Second year we put him in two afternoons a week, and then three towards the end, and now he's in the third year (age 5) and he does all four afternoons.
Interestingly, although they start school early they don't learn to read until primary school at age 6, so it really is a very different system and much less "school"-like than you may imagine.
The first day was incredibly traumatic as you had to leave your screaming child among 30 others with only 2 adults (they had had one earlier session with just 10 screaming children), but he soon got used to it and in fact has really enjoyed it. In the end I explained to the teacher that (once again) I came from a very different system, and asked that I be able to wait until someone was available for me to hand him over to personally rather than leaving him in the middle of the class.
He has made friends, many of whose parents have become our friends, and it has really integrated us into the community. He has had such a positive experience of "school", I have no regrets at all.
The other thing I would say, and what really made me decide to put him in at 3 despite my misgivings, is that I realised every other child of his age would be at school, and that not putting him in would deprive him of that social interaction. I don't know if he could have stayed at the creche, but it would have been with a bunch of 2-year-olds, and I think at home with me would have been a disaster (also I worked half-time). I did also look at a local Steiner "school" which had smaller class sizes and more flexibility, but it wasn't really "us".
Good luck with the decision, I know how hard it is.