\documentclass[border=1cm]{standalone}
\usepackage{tikz}
\usepackage{pgfplots}
\pgfplotsset{compat=newest}
% ~~~~~~~~~~~~~~~~~~~~~~~~~~~
\begin{document}
	\begin{tikzpicture}
		\begin{axis}[   scale only axis=true,
			width=.8\textwidth,
			height=.3\textwidth,
			tick align=outside,
			tick pos=left,
			xmin=0, xmax=160,
			ymin=-10, ymax=100,                 % <<<
			minor x tick num=1,                 % <<<
			xticklabels={100,90,80,70,60,50,40,30,20,10,0},
			yticklabels={0},
			ytick style={draw=none},            % from comments
			xlabel={PPM},
			title={Stylized NMR Spectroscopy},  % <<<
			]
			\addplot[black,domain=0:160] {0};               % <<<
			\addplot+[ycomb,blue,no markers] plot coordinates{
				(135,95)
				(136,45)
				(134,40)
				(110,47)
				(111,20)
				(109,42)
				(108,18)
				(40,19)
			};
			\addplot+[ycomb,red,no markers] plot coordinates{
				(136,95)
				(137,45)
				(135,40)
				(111,47)
				(112,20)
				(110,42)
				(109,18)
				(41,19)
			};
		\end{axis}
	\end{tikzpicture}
\end{document}