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$13,000 shouldn't be an issue if you have other cards with limits around there.
What's the highest limit card you have and which lender services it?
Note that Care Credit is from Synchrony and they pull TU almost entirely and generally assign a credit limit based on your TU score. So if you have a very high TU score you can probably get a higher limit.
@Anonymous wrote:
Not yet. I want to take financing in the future for a rhinoplasty. I opened 4 accounts last year and I want a couple more. But I'm worried can this affect for a decision to give me financing in the near future?
You have five credit cards already. Why would you want a couple more right now? More cards will not help your score.
You have an expensive medical procedure coming up that you need credit for. I would forgo all further CC aplications simply to increase the chances that you'll have no problem with the RP.
PS. You mention that you have $0 across all cards currently. You will improve your credit score substantially if you have exactly one card reporting a positive balance.