I am not a lawyer but I have had multiple businesses and been through many trademark exercises. Glamr should not be a conflict with those trademarks you referenced, especially if you are not competitive with those businesses. If you are a magazine super similar to Glamour, you may have more of a problem. But as long as the business is different, that name is plenty different than those two.

You can search the US patent and trademark office's database at this URL:
https://www.uspto.gov/trademarks-application-process/search-trademark-database

I searched for Glamr and it didn't return any results. It defaulted to looking for Glamor results and nothing looked like a conflict. Glam also returned no results that should be a problem for Glamr.

Obviously, it would be ideal to check with a lawyer but, in my non-expert opinion, you should be fine.