Aside from Public Record, can leans be found anywhere else?

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Hello Bigger Pockets community! Very grateful for this resource. 

We bought our first property through Auction.com and even though the process was smooth, I have been worried about encountering other leans other than what is on Public Record, which only amount to HOA fees.

This was triggered because the one thing I did not know was that 2019 Taxes were not paid (not sure if Auction was supposed to pay them but at this point they are just saying they should not have to), which increased my worry as a newbie. 

I contacted a Title Company and they offer title insurance but it is almost $2K. 

That said, my questions are:

1. How do we triple check that our Deed is clear aside from what is on public record? 

2. Since the title company mentioned they would do a full blown search on names, titles, judgements, etc, should I hire them? We received the deed and apparently the house if fully ours now but at this point I am confused. 

Any help is appreciated, especially if you remember your first deals as an inexperienced flipper : ) 
Grateful,