Could I negotiate more for my starting salary?

I am applying for a Personal Banker I position at PNC Bank and at first, the Recruiter offered me a starting salary of 45k (which would be roughly $21.50/hr), however I did a counter-offer and stated that I believe I deserve 48k (or roughly $23/hr) due to 2 reasons: Me being Bilingual (Fluent in both Spanish/English) and having prior Business background in University (even though I do not have a degree from University, I took a significant amount of Business classes + it is a very well-known and recognized University in my city)

My main question is, could I have gone higher? I ask because my current job is unrelated to Banking, it is Product Support and I actually enjoy Customer Service, I don't really mind it so no problems there. But the pay is $20/hr so to me $3 extra is alot, especially because PB I also gets roughly $2 of commission pay on top of base pay so it would be closer to $25/hr. With that being said, I think asking for a base pay of 52k or $25/hr would have been too high but I think 48k is higher but not too high if that makes sense. This is also my 1st time ever negotiating a starting pay for a job so any feedback would be great.

Pay is essentially the only reason why I want to leave my current job. I think "climbing the corporate ladder" is probably better at my current company because they say it is a breeding ground to move into Sales, Marketing, Etc. but the significantly higher pay as a PB I is alot more appealing to me compared to the $20/hr I am making right now.