if your server is sending requests to another server which has a rate limit, you'll need a global way to keep track of requests from your server, regardless of which client is doing requests to your server etc.
I would use a flat file, and save unix time and a delimiter for each request, and if the file contains ten of those, you've done ten requests, and you'll need to clean the file and remove any timestamp that is older than ten seconds, and that would give you the simplest form of a PHP rate limiter there is.
There are of course more advanced ways to this, but I'd start there, and make sure you test it so you don't loose your API access etc.