Glad you hopped in to ask us! Welcome!! Fair warning, I'm going to take a different route than usual with my suggestion for you
You need to pull your EX report and compare it to others to find out what is going on, if there is any difference in what they are reporting. You can get your free credit report (this doesn't give you a score but the score isn't necessary for this) once a year from the bureaus.
www.annualcreditreport.com is the site for this. DO NOT PAY for scores or anything else you are offered. Sites where you can see this info anytime for free include credit karma (for TU and EQ) and equifax for theirs. Again- do not pay any of them anything for this info, you can get what you need free. I use the apps for both credit karma and equifax personally.
Why did Chase deny you? EX too low? If so don't bother applying for anymore Chase cards right now. Because you have a balance you will probably not have paid off before your trip and you had trouble getting a Chase card, like I warned I'm taking a different route here and suggesting cash back is what you need at this point. The last thing you need is more points you can't convert to cash or to be stuck with a bunch of airline miles that turn out to be unusable to you. Maybe look into the Citi Double Cash?
https://www.citi.com/credit-cards/credit-card-details/citi.action?ID=citi-double-cash-credit-card There's also the Discover 5% cashback in rotating categories if you can stay on top of the category rotations
https://www.discover.com/credit-cards/cash-back/#launchCalendar from their website you can see this year's 5% cashback calendar.
Shopping portals for airline miles: unless you're using those miles switch your portal to something like topcashback where you can redeem for cash!
My thinking is obviously Cash is King for you. Cash is usable today, right now, no risk of devaluations or miles availability. (This won't get you business class flights to Europe, maybe upgraded economy I guess if you find a good cash price, but I'm concerned you won't qualify for the cards that would actually help get you those business class seats.)