It's generally a good practice to host elements important for your design (such as header, logo, banners, other images) on your own server. Quite many reasons behind it as well, first off tinypic being slow could also slow down loading on your website, second if tinypic is down that image will not load for viewers, unlike if its on your own server it will always load unless your whole site itself is down, etc. If bandwidth is your concern then just optimizing the file size and uploading it shouldn't have a negative impact on bandwidth
Edit: Additionally I notice the loading time, did a look up on your host as well, I just have one suggestion, don't fall for the "unlimited" advertising by hosts for diskspace/bandwidth! Majority (not all) hosts who offer unlimited services overcrowd their servers and you face long loading times/unresponsive sites due to so many customers on one server.