Be warned, I'm about to give this to you double-dirty BUSINESS style. I'm not going sugar coat it, pat you on the back, slap the rose coloured glasses on your head and tell you everything is fine when it clearly is not! You didn't ACTUALLY ask a question, so I'm unsure if this is even an answer, but if you brought this site to me as a client, this is what I'd tell you. To your face. I do it all the time.
If you're working in medical, depending on the country you may be subject to laws -- like the US' ADA (Americans with Disabilities Act) or the UK's 2010 EA (Equality Act) which means if you don't meet certain minimums -- like the WCAG (Web Content Accessibility Guidelines) -- you could open yourself up to civil lawsuits and/or federal fines and prosecution!
In fact, my specialty is helping major corporations, institutions, schools, and even government agencies at getting out from underneath such courtroom drama when it comes to fixing their sites.
In terms of EVERY bit of accessibility, usability, and minimum guidelines, your website is the typical disaster I'm brought in to help fix. Illegible colour contrast, goofy fancy JavaScript rubbish with zero graceful degradation, serif fonts on screen media, hard to read webfonts, and pixel metric font sizes not scaling accessibly -- and that's a cursory surface examination without even digging into the code.
Popping the bonnet, it is the typical train wreck of developer ineptitude and ignorance I've come to expect from anyone using bootcrap. Whitespace compression can't hide that level of incompetence -- there is a reason I keep telling people the ONLY thing you can learn from bootstrap is how NOT to build a website. From the stupid malfing IE conditional comments around the HTML tag(s) that Paul Irish pissed on the Internet by introducing, to the overstuffed keywords meta with zero page relevance, to the incomplete viewport meta, to the lack of media attributes on the stylesheet <link>, to endless multiple stylesheets likely sucking down more load time than the idiotic whitespace compression of the markup is saving-- it's a train wreck and I've not even gotten as far as analyzing the CONTENT!
Getting into the content -- again it's built with bootstrap.. or as many call it bootcrap. You're developer needs to go find a stick to scrape that off with if they're going to work in medical services. From the endless pointless DIV for nothing, endless pointless classes for nothing, gibberish lack of semantics, it is EVERYTHING I've come to expect from developers who don't know enough about HTML or CSS to be using a framework like bootstrap or to enhance a page with JavaScript. From the H6 that shouldn't even be on the page (since H6 means the start of a subsection of the H5 preceding it, the page has no H5, or H4... or H3 for that matter), to the lack of BLOCKQUOTE and CITE, it is clear your developer does not in fact know enough HTML to be building the front-end of your websites for you!
This is evident by the page loading 25k of white-space minified HTML (_probably around 32k without minification) _to deliver 12k of plaintext and a half dozen content images -- around 20k's job without minification given that the page is paragraph-heavy. _Mind you, "paragraph-heavy" is not a bad thing, can be quite good if it is CONTENT! _Same goes for the 80k of CSS spanning 9 files doing the job of probably 16-24k in one file, ridiculous half a megabyte of JavaScript spanning 15 files doing the job of probably 16-24k in ONE file, and massive images too blasted big to have any business on a website in the first place! Made worse by feeling like cheap stock photos mated to goofy animated nonsense giving the whole site a "sleazy marketing scam" feel.
To be brutally frank -- I'm rarely anything but -- the only thing saving you from being dragged into court is that you are not actually an insurer, not actually a medical facility, and are not an essential service.
There are a LOT of lame excuses such fly-by-night jokers will use to justify their incompetence, but there are certain minimums if you care about actually reaching people who need medical services you just do not have, and most of the techniques used to build the site are telling many visitors to your page to go perform an anatomically impossible act upon themselves!
... and that includes the notion that to meet WCAG minimums and reach as many people as possible the page should be fully functional without JavaScript altogether! GOOD JavaScript -- at least "client-side" -- aka in the browser -- should ENHANCE an already working page.
Overall not even navigating off the landing page, that site has severe accessibility woes, severe speed issues, and a relative lack of legitimate SEO whilst being burdened with poor practices that could in fact get you slapped down in search results.
Others have touched upon good questions too. WHICH CMS are you using? In-house developed? Third party? Free? pay? What SPECIFICALLY are you worried about with JavaScript given your site uses it, and ALL websites MUST use HTML -- so it's unclear what you're even asking about... though as you said, you're not a developer, you have concerns about your current one.
... and from where I sit, you have good reason to be concerned and to ask questions; Near as I can tell some dimestore hoodoo marketing scam artist AND some five and ten voodoo peddling developer have been pitching you snake oil for quite some time.