Do we need to monitor patents by other companies?

No, you don't "need to be aware at all times what kind of patents [y]our competitors are filing", but it would be beneficial to have an IP strategy also covering third-party IP.
At least, you should have a search for patent applications and patents covering your market before you launch a new product. With its launch, the product itself becomes prior art for later patent applications. However, there is still the possibility to miss relevant patent applications, because they are published 18 months after filing.
Better, you should have regular search for a defined profile (covering competitors as well as technology - as relevant rights may originate from non-competitors) providing a reasonable / manageable number of identified patent applications and patents (hits). Ongoing evaluation of the hits serves as early warning and may avoid surprises when the product in ready for launch. Moreover, the identified patent applications and patents could serve as general source of inpiration - without adopting any protected solutions, of course.
For help with third-parts rights as well as your inventions, find the right specialist: a patent attorney whom you like and find trustworthy.
Please feel free to get in touch.

You should definitely monitor patents by others in your field for primarily two reasons: 1) such patents will determine the likelihood of you obtaining your own patents for similar devices or technology because such patents and/or published patent applications will comprise prior art which can be cited against the claims of your patent applications; and 2) you need to know if you potentially infringe any other patents. Also note, contrary to some generally assumed incorrect positions or understandings, obtaining your own patents do not necessarily mean that you are free to make, use, or sell your own patented devices or technology - to the contrary, you may be infringing other patents even though you were granted a patent for an "improvement" in your art or field. Obtaining a patent only confers the right to the patent owner to exclude others from making, using or selling the patented device or technology - it does not confer that right, of making, using, or selling, the patented device or technoogy to the patent owner.