You don't need to check the whole 62*62*62*62 addresses online through API. That would be an insanely long journey, and you'll get blacklisted at any free service before finding what you seek, no doubt.
In your place I would:
1) download the daily balance snapshot from blockchair.com
2) either in Windows through Cygwin or in Linux shell, or in MacOS terminal type:
zcat blockchair_bitcoin_addresses_latest.tsv.gz|grep "the part of the address you remember"
Example, I took a random address from the list and removed last 4 digits:
root@ubuntu:~# time zcat blockchair_bitcoin_addresses_latest.tsv.gz |grep 1EpfyhhNnwF2Sv53PUzoJGRawiTVy
I've run the command with
time in front just for testing purposes, in order to demonstrate that it took less than 10 seconds to parse the list and find the matching address, and this is not a powerful PC. I don't even have SSD here, I bet if you have one it will be even faster.
Please note the number 1 after the address: this BTC address has indeed 1 satoshi.
If you are in doubt about capital letters in your address just add the
-i option after
grep so it will not run a case-sensitive search and will return the result even with wrong capitals in the search pattern; here I searched all Bitcoin addresses with non-zero balance containing my name despite any capitals, and it still took 10s:
root@ubuntu:~# time zcat blockchair_bitcoin_addresses_latest.tsv.gz |grep -i marco
Relevant note: if you have not a premium API account on blockchair.com the list download (today over 700MB) is rate limited to 128KB/s. The DL takes around two hours but it is updated daily, and I find it's still a tremendous booster for all bulk balance lookups issues, unless you need balances to be real time. In this last case, look to a paid API as only solution.