I see this: https://en.wikipedia.org/wiki/Filter_bubble
So if I search for keywords related to my website to check the actual rank will the results be biased?
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While you can't remove all the factors a search engine will use (the one most impacting you will be geographic targeting), you can get a relatively clean search result by using a separate browser. One with no browsing or search history, no cookies, and not logged into whichever search engine you're checking. That will remove much of the search engine's personalisation of the search results.
You can get around the geographic location targeting on Google by using a tool in Ads. Google Ads Diagnosis and Preview tool allows you to specify a location to search from, and gives you the organic results along with the paid ads.
Beyond that, you have to rely on Google Search Console's Average Position metric, which will tell you where your website appears in the search results for some searches.
There are third party tools which will run tests for you on an automated basis. My personal experience of these has been mixed and I'd hesitate to recommend any. Just search for Search Position Tracking and try a few out (they mostly offer free trials, either time or functionality limited) to see if they're of any use to you.
On final point, do bear in mind that your website's visitors will have their search results tailored by the search engines based on their search and browsing history. So what you see won't be what they see. It'll just be a fair approximation.