in other words if price increase fee will increase to be more than sending amount
The network is getting congested due to low fees and if this continues then paying low fees means that you might have to wait for several days before the transaction even gets a single confirmation. However this does not mean that you have to increase fees if price of bitcoin increases. It depends on how much everyone else is willing to pay and that competes with the amount that you pay for your transaction.
In other words if you are not willing to provide a high fee then other people's transactions will confirm before your transaction does.