I do not think that the increase in price has anything to do with the number of searches about a particular product on any eCommerce portal, since the prices of a product are decided by the seller and not by the eCommerce portal. Ecommerce portals charge the seller for the services offered by them to the seller and services availed by the seller.
There can be various factors contributing towards increase in the price of a product after a few days:-
1. Demand & supply:- If I were a seller, I would keep on increasing price of a product gradually, if the product is not available in the market and I have the product in stock.
2. The buy-box is generally allotted to a seller whose price is the lowest. Of course, other factors too play a role in it.
Now suppose a product is being sold by ten sellers on a site at different prices (e.g. A @ 310, B @ 325, C @ 350, D @ 360 .....). Now the seller A has the lowest price, 310, and he gets the buy box. Suppose he has 25 pieces in stock, so he fills in his inventory as 25 pieces. One adds the item to his cart on Sunday to buy it later on Wednesday. The seller A's 25 pieces are for sale for other buyers too.
By the time, Wednesday in this case, you try to buy the product, the inventory of seller A is sold out. So, his name automatically gets removed from the line and the next seller in line, seller B with a price of 325, gets the buy-box. So, when you log-in on Wednesday to buy the item, you see the price tag of 325.
So, you think that the price has been increased because of your searches, whereas it is not the reality. On the contrary, you may benefit if you keep on searching for the same item or add it to your cart and leave it there. The eCommerce sites keep a tab on your searches and your IP. If you keep a product in your cart, sometimes they offer you a discount on the product in your cart.
3. Increase in charges levied on seller:- There is a chance that there is an increase in VAT/GST or the commission charged by the eCommerce portals between the period you add an item to your cart & you go for making the payment or buying the product. The seller will adjust his prices accordingly.
In that case also you will find an increase in sale price of a product.
Hope it suffices!
When you talk, you are only repeating what you already know. But if you listen, you may learn something new!