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Yes, will just take a bit of time but no long-term damage. Inqs are over-feared by some!
The two solid rules:
1) Inqs drop off entirely after two years
2) Inqs stop impacting FICO score after 1 year.
And the impact on the score reduces in the first year, certainly after 6 months it is less.
Some issuers look only at inquiries in the last few months, others look at all those on the credit report. But you really don't have a huge number, and, as others have suggested, in 6 months or so, it will be fine.
You'll be fine...just stay in the garden, and spray yourself with lots of Off to keep the App Bug away from you!!!!
Congrats on your new credit. I've been there. I did something similar early last year. Let the accounts and inquiries age a little bit. It made it easy when I pretty much avoid anything that would "trigger" me to want to apply for new credit. Once you build your history and let the inquiries age, you'll be back to getting approvals again. Good luck.
I agree with the other posters. You just need some gardening time.