ideally, you could post a link to your site; that makes helping with formatting/css issues easier.
the searchform position is defined in style.css, for different situations:
/* Search Form */
#branding #searchform {
position: absolute;
top: 3.8em;
right: 7.6%;
text-align: right;
}
and
#branding .only-search #searchform {
top: 5px;
z-index: 1;
}
and
#branding .with-image #searchform {
top: auto;
bottom: -27px;
max-width: 195px;
}
you have to redefine this in style.css of your child theme;
example (adapt the numbers for your needs):
#branding #searchform {
position: absolute;
top: auto;
bottom: -30px;
}
(you might need to redefine somthing for the other situations as well – no idea where they are called)