Nginx ssl configuration for subdomain - ssl

Question

I have a website and multiple subdomains. On each subdomain, except one, I use a CMS that generates it's own ssl using Let's Encrypt. On the remaining subdomain I want to add my own certificate from Cloudflare. I generated a certificate put it in my /var/www/my/ for now. Just for testing. And in nginx I configured this block:
server{
listen 443 ssl http2;
listen [::]:443 ssl http2;
ssl_certificate /var/www/my/fullchain.cer;
ssl_certificate_key /var/www/my/my.domain.com.key;
root /var/www/my;
index index.php index.html;
server_name my.domain.com;
location / {
try_files $uri $uri/ =404;
}
location ~ \.php$ {
include /etc/nginx/fastcgi_params;
fastcgi_pass unix:/run/php/php7.0-fpm.sock;
fastcgi_index index.php;
fastcgi_param SCRIPT_FILENAME /var/www/my/$fastcgi_script_name;
}
location ~ /\.ht {
deny all;
}
}
There seems to be a problem with my implementation because now my.domain.com works but for everything else I get this error from Cloudflare: Error 525: SSL handshake failed.
Any ideas what I'm doing wrong?
Thank you
EDIT:
This is the conf file from the CMS. THis is how they set the certificate.
server {
listen 443 ssl http2;
listen [::]:443 ssl http2;
server_name sub.domain.com;
root /var/www/sub/system/nginx-root;
ssl_certificate /home/domain/.acme.sh/sub.domain.com/fullchain.cer;
ssl_certificate_key /home/domain/.acme.sh/sub.domain.com/sub.domain.com.key;
include /var/www/sub/system/files/ssl-params.conf;
location / {
proxy_set_header X-Forwarded-For $proxy_add_x_forwarded_for;
proxy_set_header X-Forwarded-Proto $scheme;
proxy_set_header X-Real-IP $remote_addr;
proxy_set_header Host $http_host;
proxy_pass http://127.0.0.1:2369;
}
location ~ /.well-known {
allow all;
}
client_max_body_size 50m;
}