Elliot, there are several other soccer fans here, being as there are a lot of Brits who are members. Barry (BAZ) is an Aston Villa fan, and I, for my sins, happen to support the Wolves, aka Wolverhampton Wanderers, currently languishing in the Championship division, or the old secend division as it used to be. At least we are top of the table, have a good team, a good manager, and are likely to be promoted at the end of the season to mix it up with the likes of Arsenal, Chelsea, Liverpool, et al in August.
ARSENAL? There is a standing joke in the UK, that one supports their regular team, and whoever happens to be playing Aresnal or Chelsea that week. Everyone loves to hate Arsenal!!! They do play some very pretty football though, no question.
A suggestion: Research which teams are playing Arsenal at home during your stay, and try to buy tickets to that ground....... You will get to see the Arsenal play, but not at the Emirates. Suggestion Two: Write them a letter! Explain that since you are in the USA, you are unable to obtain the tickets to see a game in the conventional manner, and enquire if you could buy tickets to see the game any other way, the circumstances being exceptional and all.
I shall see if there is anything I can do for you. No promises, but I can put the word out. Problems is, they are playing Fulham on the 28th, which being a local derby means that tickets will likely be sold out.
On the 3rd of March they are against West Brom in the cup, at West Bromwich. West Brom also play very attractive football, and so this may be a good game to try to see. You may be able to get tickets to the game through West Brom's website, and it is a comparatively short train ride away from London.
https://www.wba.premiumtv.co.uk/page/TicketNews/0,,10366~1536780,00.html