The good news is you probably don't have any bad credit marks (assuming you have no late payments, right?).
The bad news is credit takes TIME and PATIENCE. I'm assuming that you were declined for all 3-4 cc's and loans you applied for? You need to give some time to establish and build your credit history. Make sure to use your cc, pay it off in monthly installments -or- in full every month.
You CAN get approved for an Amex Blue cc but I would suggest two things:
1) Read the Amex Blue decline letter you're going to receive and the 3-4 previous letters, notice a trend?
2) Every new cc or loan you apply for is an inquiry on your credit, regardless if you are approved or declined - several inquiries is a BAD thing and lowers your credit score. So here's the bad news you don't wanna hear, in order for you to establish credit with your VISA and have the 3-4 inquiries disappear you need to wait at least 12 months. By then you will have proven that you're responsible with your VISA and the 3-4 ccs you applied for will drop off.
This is a conservative approach but it's what I always recommend to my clients. I've worked in banking for nearly 8 years, 4 of which were spent in Consumer Credit/Home Equity/Auto Financing.
Use your VISA, pay it off, DO NOT APPLY FOR ANY NEW cc's and wait for 12 months then apply for an Amex Blue.