The short answer is yes. Although the boutique really should have given you one! You can apply for one on your own, and it is my understanding that for certain cases (e.g. for commercial purpose such as re-selling the bag) a new one would be required regardless of the old one from the boutique (as the old one from the boutique does not cover the new purpose). For personal use items traveling with you, often there are exemptions from needing a CITES, but again I always err on the side of caution and probably would have mine (photocopies and all, along with receipts) even if I had checked that both the country I’m going from and going to have exemptions; besides just the CITES requirement it’s also about proof of where I’ve purchased these items & that these are my personal use items.
To get to the original question though; if for whichever reason you are in a case where you need to apply for one, the how depends on the local CITES issuing authority and what their specific rules and procedures are, and may go from fairly straight-forward (fill out some form, know your specific species’ scientific name, etc.) to pretty complicated (not to mention slow because government agencies. I think the USA website says something like “60 days”; although I’ve never done it myself and maybe they work faster in reality lol). Most countries’ department should have a CITES section on their website with information on whether you need one + how to apply for one. When in doubt I would contact the authority and ask for official clarifications on anything unclear.