DB Transaction: can we block just a record, not the whole table?

I am trying to insert the data into the Wallets table of a SQL Server database. There are can be many requests at the same time so due to the sensitive info I have to use transactions.

The work flow is the following:

1. read the amount of the user's wallet

2. insert the new record based on the previously received data

I tried different isolation levels but in all the cases the transaction blocks the whole table, not just the record I am working with. Even ReadUncommitted or RepeatableRead block the whole table.

Is there a way to block only the records I am working with?

Let me detail: I don't use any indexes in the table

The workflow (translating C# into SQL) is the following:

1) Select * from Balance 2) Insert ... INTO Balance